Efficient Management of Transcoding andMulticasting Multimedia Streams

A. HenigComputer Science Department TechnionHaifa 32000, Israelcshenig@cs.technion.ac.il

D. RazComputer Science Department TechnionHaifa 32000, Israeldanny@cs.technion.ac.il

AbstractManagement of multimedia applications is a very challenging task. This is especiallytrue in the emerging new Internet where users use devices such as smart phones andPDAs, a considerable amount of them are connected via wireless connections, and peerto peer applications are becoming more and more popular. In this new environment, themultimedia format that should be sent to different users varies considerably and sendinga media stream to a set of users often involves transcoding of formats.

This paper addresses the problem of managing multicast streaming in this new envi-ronment by defining a framework in which transcoding can be done in internal networknodes, and not necessarily at the sender’s or at the receivers’ ends. In this frameworkthe sender retrieves all the information regarding the transcoding abilities of the variousnodes and the characteristics of the links. Then, it needs to decide how to broadcast themultimedia stream, in what formats, and where to perform the needed transcoding.

We show that this algorithmic problem is NP-hard (and also hard to approximate).However, for the very practical case where the number of relevant formats is small, wepresent an efficient approximation scheme. We study, using simulations, the actual perfor-mance of our algorithm and compare it to transcoding at the sender’s or at the receivers’ends. Our results indicate that performing transcoding in intermediate nodes is indeed ef-ficient, and that our algorithm can find a much better streaming scheme than any knownalgorithm.

KeywordsNetwork management, approximation algorithms, streaming multicast, Steiner tree

1. Introduction

One of the important functions of the Internet is the capability to deliver live audio andvideo streams to users at high quality, fast speed and most important - low cost. Deliveringlive streams across the Internet is becoming more and more popular as computers gradu-ally replace other media and entertainment channels such as radio, television, newspapersetc. Newly developed standards and encoding technologies, such as AVI and MPEG, havemade it possible for users to receive television-quality video with various data rates andvarious bandwidth consumptions. In today’s heterogeneous environment, end-users usedifferent devices such as laptops, PDAs, smart phones and others. In this environment,sending customers media objects forces the sender to supply the data in different formats

0-7803-9087-3/05/$20.00 ©2005 IEEE

to be properly accommodated by the end users’ devices. It is reasonable to assume thatthe multimedia information was not initially encoded in all formats, therefore, in orderto suit the clients’ devices in terms of CPU availability, screen resolution and others, themultimedia data should somehow be transcoded.

There are two additional characteristics of the Internet that are extremely relevant tothis discussion. The first is the increasing number of wireless and cellular users that areconnected to the Internet. Most of the small devices (laptops, PDAs, and smart phones) areconnected either through WiFi (802.11) or various 2.5G and 3G cellular technologies. Thewireless connection bandwidth and other parameters such as loss and jitter have a crucialimpact on the quality of a media stream delivered over this connection. Another importantaspect is the move toward overlay networks and Peer to Peer (P2P) applications. Moreand more applications (currently mainly file sharing applications but in the future alsomultimedia applications) are based on the P2P paradigm where information is transferredbetween end users and not between users and well defined servers. When a media streamis sent from a user to a set of other users, one can no longer assume (as in the case of awell equipped server) that the sender can transcode the data to all possible formats.

Transcoding is defined as a transformation that converts a media object from one formto another, frequently trading off object fidelity for size [16]. It can be executed at vari-ous components in the network such as servers, proxies, and clients. At each component,the cost of the format transformation is different. Placing transcoders at the end-userswill preserve the network architecture and will transfer responsibility of the format trans-formation to the clients. However, this option can be very expensive due to limitationof connection bandwidth and computational power, and in some cases even infeasiblesince the client may be unable to recognize the sent format. Putting the responsibilityfor reformatting at the server’s hands can also be an expensive option causing the serverto store all formats to each file and wait for clients’ requests. If the server chooses totranscode the files only when clients’ requests are issued, this can cause a considerabledelay in delivering time. We should also remember that servers are usually one of thenetworks’ bottlenecks, especially when media delivering is considered, thus loading themwith expensive computational tasks before serving each request will only increase theirinstability. In addition, the increasing popularity of P2P applications results in a situationwhere many of the multimedia stream’s sources are not really servers but rather low enduser devices. The third option is to transcode the media objects at intermediate nodes inthe network. This approach was explored extensively in the past (see for example [8, 10]),under the assumption that intermediate nodes (mostly proxies and even routers in the fu-ture) have the capability to transcode requested media objects according to the end-usersspecifications.

Managing multimedia streaming in this heterogeneous environment is a very challeng-ing task. As always, good management is composed of acquiring the needed information,using this information in order to derive the correct decisions, and making sure that thesedecisions are indeed being deployed. In the Network management framework, the firsttask is usually referred to as monitoring; the second task is the algorithmic aspect of themanagement system, which results in policies that have to be enforced over the networkelements. An interesting question in this case is who is responsible for the management

426 Session Nine QoS Composition and Adaptation

of the multimedia streaming? On one hand, the application itself has the knowledge aboutthe clients, their preferred formats and the server’s capabilities and can control the steam-ing process. Therefore, the management should be done by the application. On the otherhand, network related information (such as available bandwidth, and information regard-ing the transcoding capabilities of internal nodes) may be known only to the network (orto the network management system), and therefore managing the multimedia streamingcan be a component of the network management system.

In this work we chose to put the management responsibility on the media source. Asexplained above, this entity has access to both server and client information, and bestknowledge regarding the format needed. One has to define methods through which thismanagement system can gain network information and learn about the various transcod-ing capabilities of the different nodes, and the various parameters (i.e., bandwidth, loss)of the different links. This can be done using services such as IDMAPS [13] that pro-vides information about network distances and links characterizations, and using capabil-ity discovery protocols (like the one described in [6, 19]). In this “discovery phase” thesource, who wants to send the data, discovers the capabilities of the different clients anddecides which media formats may serve each client. Each option, described above, regard-ing where to perform the needed transcoding, has its own advantages and disadvantages.In order to be able to decide where to perform the transcoding, and how to multicast themultimedia stream, it is wise to look at this problem as a simple question of cost (see [6]).

The cost of sending a media object to users is composed of mainly two components:First, the cost of the transcoding operation aiming at supplying the user with his/her com-patible format. Second, the communication cost of transmitting the streams over the net-work. The transcoding cost, itself, is a function of three parameters, the two formats thatthe transformation is dealing with (the origin format and the produced format), and thenetwork node in which the transcoding occurs. Choosing the best network node to performthe transcoding is crucial since the network is very heterogeneous even when consideringonly intermediate nodes. Not all intermediate nodes have the same computational power,thus it is reasonable to assume that a specific transformation would take longer time at acertain node compared to other nodes, meaning, it will cost more. The converting speed ateach node is not considered as an additional separate cost, but rather taken into account inthe general transcoding cost of that node. A third element that may have influence on theoverall cost is the storage of the media file. This element is less important when dealingwith live streams and will be regarded as covered by the capability discovery protocol.Meaning, this protocol will chose in advance only formats that are compatible with thestorage capability of the clients. We will not consider this cost as an additional parameterin our problem.

This paper focuses on the algorithmic problem that lies in the heart of the multimediastreaming management problem: How to multicast and what transcoders to use in orderto guarantee the efficient delivery of the needed format to each client. The solution of thisproblem should contain the following information. What is the best routing tree for ourmedia stream starting at the source and ending at each client? Where should transcodingbe performed on that tree? Which specific format (out of the formats the client can decode)should be delivered to each client? What is the overall cost of the solution, and how

427Efficient Management of Transcoding and Multicasting Multimedia Streams

good is it?. In this paper we propose a novel approach to solve all these questions byformulating one single optimization problem. The solution to this optimization problemwill automatically reveal all the answers as we explain later.

The optimization problem we formulate for this discussion is NP-hard and cannotbe approximated within a reasonable guaranteed factor of log n, where n is the numberof receivers. However, in practical scenarios, the number of relevant media formats isrelatively small (5-10). Using this observation we present an approximation algorithmthat finds a solution to the above problem with a cost that is guaranteed to be at most aconstant factor times the number of formats from the optimal problem.

We then examine the actual performance of our scheme and of the proposed algo-rithm in several scenarios. First we demonstrate using both a very simple network, anda network simulating the US backbone, that transcoding at intermediate nodes is indeedbeneficial. Then we show that our algorithm outperforms other algorithms and find mul-ticast trees and transcoding schemes with much better cost. This is done on medium sizenetworks and real life formats.

The main contributions of this paper are the developments of the novel approach forplacing transcoders at internal nodes, the approximation algorithm with its guaranteedapproximation ratio, and the demonstration of the applicability of our results.

The rest of this paper is organized as follows. In the next section we examine some ofthe relevant related work. Then in Section 3, we define the formal problem, in Section 4 wepresent our approximation algorithm and in Section 5 we present our simulation results.We conclude this paper with a short discussion in Section 6.

2. Related Works

The problem of efficient transcoding techniques was addressed by many works. Pa-pers dealing with this problem can be divided to three groups: Those dealing with thetranscoding algorithms themselves, as in the case of converting MPEG-2 to MPEG-4 [11],those dealing with systems’ architecture, as in the case of TeC (Transcoding enabledcaching) [1], and those dealing with efficient proxy placement on the path between theserver and its designated clients. Our work belongs mainly to the last group.

Previous research on proxy placement concentrated mainly on unicast sessions [16,15, 4]. As far as multicasting media is concerned researches have initially focused on an-alyzing its general concept, its advantages and disadvantages as in [20]. Lately researchhas shifted toward the actual construction of multicast media systems. This constructionhas many times dealt with specific use of special network components as in [17, 22]. Inthe later, for example, Rubenstein et al. have tackled the issue of repair servers which aimsat ensuring reliable media delivery. In [23], the issue of “interest filtering” achieved bythe deployment of content base filters in a “Specialized Active Networks for DistributedSimulation” (SANDS) was examined. Though the use of many special purpose compo-nents was studied extensively , the question of their exact placement to ensure minimumoverhead was not addressed.

Recently, Dabran et al. [6] studied management aspects of multimedia email attach-ments. They studied a similar problem to ours where the sender has to decide whether to

428 Session Nine QoS Composition and Adaptation

transcode the attachment file or to send it to the receiver in the original format. We adaptsome of the formulation and modelling from this work; however in our case the situationis different. To start with, we deal with media streams and not email attachments. Moreimportantly, we allow transcoding in intermediate nodes, and thus the network topologyis an important part of our input. Moreover, in [6] the authors used a non-polynomialalgorithm to search for the best possible transcoding scheme, here, we develop a novelapproximation algorithm since we have many receivers and not just one receiver andsender as in [6], thus, exhaustive search is infeasible.

Theoretically speaking the issue of proxy placements is related to the well knowngroup of optimization problems called Facility Location. Problems in this group dealwith efficiently placing of facilities (in a plane or in a graph) in a way that will bestserve potential clients of those facilities. Another theoretical group of problems that has avast impact on this work is the “Steiner Tree Problem”. The use of multicast connectionsminimizes the cost of sending the same data to a group of users. This minimization can beaccomplished by sending the data via a tree with a minimum cost edges which connectsthe data sender to all the designated clients. The question of how to build such a tree is theSteiner Tree problem. This is actually a group of problems which has many variants, allwere investigated thoroughly in the past [14, 21, 25]. Our transcoders’ placement problemcan be seen as an instance of these two groups combining characteristics from them both.

3. The Transcoders’ Placement Over Multicast Networks Problem

Our problem deals with multicasting a media object from its source to a group ofrecipients over a network. We assume that each node in the network has a multicastcapability and some nodes can host transcoders and perform transcoding operations.Our goal is to explore the question of placing transcoders in the network in a way thatallows users to receive the multimedia data in their required format, at the lowest possiblecost. We name this problem the Transcoders’ Placement over Multicast networks, orin short, the TPM problem. The TPM is an optimization problem in which we wish tominimize the overall cost of delivering the data from the source to all its clients. The costof the data transmitting includes both the transcoding cost and the communication cost,as explained before. Note that in order to minimize the cost of delivering the media indifferent formats, the routs that are most likely to be chosen can be different from thosethat would have been chosen by a simple Layer 3 multicast protocol. We assume that themedia origin (the source) has the ability to learn about its clients devices’ capabilities (i.e.which media formats may suit each client) and about the capabilities of the intermediatenodes to transcode the media streams. We represent the media conversion ability of thenetwork nodes by formulating converting graphs. The converting graphs are directedweighted graphs in which each node reflects a different media format. The directed edgesof these graphs represent transcoding abilities and their compatible cost. Such graphsappear in the right hand side of Figure 1. Since each network node can have differentconverting capabilities and different converting costs, each such node is associatedwith one specific converting graph. Note that the maximum amount of nodes in eachconverting graph cannot exceed the total amount of formats recognized by all nodes in

429Efficient Management of Transcoding and Multicasting Multimedia Streams

the network. Following this explanation of the converting graphs we can now formulatemore precisely the TPM problem. We would like to build a minimum spanning tree overthe network which connects the media source to all clients while traversing several nodesthat have the required transcoding capabilities according to their converting graphs. Oursolution’s cost consists of the edges we have chosen to traverse on in the network, andthe cost of the directed arcs chosen in some of the nodes converting graphs. It is possiblethat in order to minimize the overall solution’s cost we will choose several formattingprocedures between a source and a designated client. The TPM problem can thus beformulated as follows:

TPM Problem Definition: We are given an undirected weighted graph GTPM = (V,E),which represents a multicast supporting network, and a group of weighted directed graphseach formulated like this Gconvert = (t, V, E) and represents a format converting abilityof some node t ∈ V TPM . We are also given a set of nodes C ⊂ V TPM representing theclients and a root node r that represents the media source. Each client in the network hasthe capability to receive a subset of formats from a large group of formats F supported byour system. As we stated above, the elements in F = {f1, f2, ..., fF } are the convertinggraphs’ nodes.

The weight function (w+ : E → R+) of GTPM represents the basic communicationcost on each link. This cost is liable to changes according to the media formats sent onthe links. It is reasonable to look at the relationship between the basic link cost and themedia format as a simple multiply function: w(e) = e · fi. According to this formula wecan assume that the original media stream format has a value of 1 (f1 = 1) and all otherformats are representing some compressed encoding of f1, thus, (∀i fi ≤ 1).The TPM objective is to create a minimum weighted tree TTPM which connects the rootnode r ∈ V TPM to each client, and traverses over transcoders located in some of V TPM

nodes. The final format reaching each client should be one of the client’s subgroup ofcompatible formats.

A solution to a TPM problem should include many elements: The shape of theminimum spanning tree over GTPM , a group of nodes in V TPM in which transcodersshould be placed, the exact format which was delivered to each node and finally, theoverall cost of the solution. We will now introduce an equivalent presentation of theTPM in which the shape of a resulted spanning tree will automatically reveal the entireset of elements we mentioned above. This new presentation includes a multi layeredmixed graph (MLMG). A mixed graph is a graph with both directed and undirectededges [7]. Our presentation is best described in Figure 1. Each layer in the MLMG hasthe same structure as the original undirected GTPM , whereas, the layers, themselves, areconnected to one another by directed edges. These edges, connecting copies of some nodet ∈ V TPM , for example, are actually the edges of node t’s converting graph. Thus, theMLMG’s layers are representing changes of formats occurs while deciding to traverse onsome directed edge. The amount of layers in the graph is exactly the amount of formatsin F . Note that copies of the same undirected edge in different layers have different costas a function of the exact layer in which it is found. This cost is a multiplication of some

430 Session Nine QoS Composition and Adaptation

Figure 1: A Multi Layered Mixed Graph (MLMG) representation of the TPM problem

basic cost e and the format fi where i is the layer’s index and∨

i={1,..,F} fi ≤ 1. It isreasonable to order the layers in the MLMG in an increasing compression form where1 = f1 ≥ f2 ≥ ... ≥ fF . Following this form the graph’s top layer represents the mediaorigin format and each layer beneath represent some compressed format of the origin.The media source in the MLMG is the root’s node copy found at the top layer (alsorepresented as r1 - the black node in Figure 1). The clients (C ⊂ V TPM ) are the dummynodes found to the left and right of the main MLMG structure. These dummy nodesare connected by zero weight directed edges to copies of the same node that previouslyrepresented the client in the original graph. Copies of that node can be found at the layerscompatible to the formats excepted by the client. A solution to the TPM problem overthe MLMG should connect the top layer’s root node to each one of the dummy nodesrepresenting the clients. This solution must be optimal in terms of its cost.

Claim: Any optimal solution for the TPM problem over the MLMG, has the samecost as the optimal TPM solution on a regular network representing graph.

This claim is obvious since there is a one to one mapping between regular TPM span-ning tree which includes traversing on converting graphs and a spanning tree created onthe formulated MLMG.

4. An O(F) Approximation algorithm

Using a simple reduction from the “Steiner Tree problem” on undirected graphs, it iseasy to see that the TPM problem is NP - hard. The Steiner tree problem is NP-hardand remains so under a broad range of restrictions [12]. A TPM problem with only onemedia format (|F| = 1) which is accepted by all clients and sent by the source is exactlythe undirected Steiner tree problem. Since the TPM is NP-hard we cannot hope to findan algorithm that creates an optimal solution in polynomial time. An obvious approach,therefore, is to use an approximation algorithm that will find, in polynomial time, onlya sub-optimal solution in terms of cost. An algorithm A is an r(n) − approximationalgorithm for a minimization problem, if for all instances of that problem the cost ofthe solution produced by A is no more than r(n) times the optimal solution. One can

431Efficient Management of Transcoding and Multicasting Multimedia Streams

show that even when using approximation algorithms for the TPM problem we can notguarantee a better approximation than log(max(n, F )), where n is the number of clientsin the problem instance and F = |F|. For lack of space we do not present this proofhere but rather focus on an algorithm which establishes an O(F ) approximation result.Note, that practically speaking it is our preference to solve the TPM problem by usingan approximation ratio in the size of F and not n the amount of clients since in mostnetworks |F| << n.

Before presenting our algorithm let us note that the TPM problem formulated on anMLMG has an obvious approximation algorithm. If we consider the entire graph as a di-rected graph (each undirected edge will be transformed to two opposite directions edges)we can use a directed Steiner tree approximation algorithm to solve our problem on theMLMG and to connect the graph’s root to each and every client. There are several knownapproximation algorithms for the directed Steiner tree problem [2, 25]. However, thebest approximation achieved for this problem is only O(nε) where n is the number ofclients [9].

Algorithm BF (for Bounded Formats) describes a method for creating a near optimalspanning tree which connects the media source (the root node) to all clients while sup-plying each client with a suitable media format. The algorithm runs on the Multi LayeredMixed Graph (MLMG) created by a given TPM instance and works in three phases onwhich we will now elaborate:In the first phase the algorithm chooses the best format for each client out of the groupof formats the client is capable of receiving. Suppose that a specific client can receive agroup of formats G ⊂ F . Our algorithm will choose for that client a single format fromG which is accessible by the shortest from the root node. This path is calculated on thecreated MLMG. After choosing this format, we can erase the dummy node representingthe client and all edges connecting to it. We replace dummy node by a new node whichnow represents this client in the appropriate level. We can now consider the problem as ifeach client can accept only a single multimedia format.The second phase of the algorithm runs over the MLMG’s layers and at each layer1 ≤ i ≤ F it connects the local copies of the terminals that exist at that layer. Theseterminals are the nodes who’s format were chosen to be the one represented by layer i.Connecting the terminals is done via an undirected Steiner tree. Since finding such a treeis NP hard, we use an approximation algorithm for the undirected Steiner tree problem.Currently the best known scheme for this problem is due to Robins, G. and Zelikovsky,A. [21] and achieves a 1.55 approximation result. However, we can settle with a muchsimpler algorithm which guarantees a factor 2 approximation given by a minimum span-ning tree in which shortest paths between terminals act as tree edges [12].In the third and last phase of the algorithm we connect the spanning tree created at the toplayer to the spanning trees created at layers beneath using the shortest available path.After finishing all three phases the algorithm outputs the spanning tree we have just cre-ated and it’s overall weight, i.e. the solution’s cost. Note that it is possible that severalMLMG edges will be counted More than once, both for an undirected Steiner tree atsome layer, and for some shortest path calculated at the third phase. Our algorithm willnot count duplicated edges twice.

432 Session Nine QoS Composition and Adaptation

Algorithm 1 (BF): 2(2F−1)K - approximation TPM Algorithm

i = 1; {The top layer}S = ∅; {A structure for holding the various trees}costBF = 0;Tree = ∅;PHASE 1:for all c ∈ M do

Pj ← The Shortest path from r1 to c.{Can be calculated using dijkstra’s algorithm [5] for example.}delete the dummy node c and all directed edges connecting to it.ci

j ← The new node to represent client c which is found at layer i and was chosen by Pj .{The last node inPj before the dummy node of client c.}

end forPHASE 2:while i ≤ F do

Si ← A steiner tree connecting all terminals in Ci. {consider the original root node (r1) as one of C1 terminals.}Tree← edges of Si

i+ = 1;end whilePHASE 3:p = ∅ {A structure holding F-1 paths}i = 1while i ≤ (F − 1) do

pi ← the shortest path connecting S1 to Si+1

Tree← pi - Avoid edges added in the previous step;i+ = 1;

end whileCostBF + = Cost(Tree);Output:CostBF , Tree;

For lack of space we don’t present an explicit analysis of the above algorithm but statethe final outcome:

THEOREM 4.1: Algorithm BF is a polynomial time 2(2F−1)K approximation algorithm

for the TPM problem, where F = |F| and K is the maximal compression ratio amongformats in F - (K = fF

f1).

As pointed out before, our algorithm outputs a spanning tree on the MLMG. From thisspanning tree one can retrieve the answers to all the questions we mentioned in the intro-duction. More specifically, a vertical edge from layer fi to layer fj in node u representstranscoding from format i to format j in node u. An horizontal edge from node u to nodev in layer k indicates that the file in format k should be sent from node u to node v. Theoverall cost of the MLMG spanning tree is the overall cost of the TPM solution.

5. Simulations

In this section we demonstrate the practical importance of the TPM problem and the ad-vantages of our algorithm.We first consider a simple example which shows the advantages of transcoding at inter-mediate nodes in the network. Figure 2a depicts a simple star shape graph which contains8 nodes in which node 1 represents the media origin (the root) and nodes 2 to 7 representthe clients. The media file was originally encoded in format f1 but the clients (v2, ..., v7)would like to receive it in another format f2. We assume in this example that all vertexesin the graph, except the source, are capable of hosting a transcoder to convert format f1 to

433Efficient Management of Transcoding and Multicasting Multimedia Streams

Figure 2: A simple example for our TPM problem

f2∗. The conversion cost is the same at all nodes, furthermore, there is no compression,

i.e., f1 = f2 = 1. Let us consider now two options of delivering the the correct format(f2) to all clients: Option 1, send the media file in the original format, f1, from the sourceto all clients and convert the format to f2 at the clients themselves. Option 2, send the me-dia, in its original format, from the source to the intermediate node 8 in which the formatconversion to f2 will take place. Then, continue to deliver the media in the new formatto all the clients. Figure 2b depicts a comparison between these two strategies. Note thatoption 1 uses 6 connection links (marked by solid edges) and 6 conversion operations todeliver the media, whereas option 2 uses 7 different connection links but only one con-verting operation. In general, if sending the media file from the source to the clients costsmore than the formats’ conversion then it is preferred to use less connection links butmore transcoding (as was offered by option 1). This claim should of course be reversedif transcoding costs more then the media delivery. In that case, option 2, which convertsonly once, should probably be chosen. Figure 2b depicts the cost of the two options as afunction of the ratio between connections’ and conversions’ costs. One can see that as theratio increases, meaning, transcoding costs more than traversing over the communicationlinks, it is cheaper to transcode at some intermediate node than to transcode at all clients.Note that in our cost function we combine transcoding cost and communication cost. Insome cases this combination is very difficult since each one of them deals with a com-pletely different set of resources. As a result the ratio between the basic communicationcost and the basic transcoding code is an indicator to the importance of each one of thecost component in the overall evaluation, and the tree found by the algorithm depends onthe value of this ratio.

The second set of simulations, shown in Figure 3, depicts a practical implementationof the TPM problem and our BF algorithm. Consider the network demonstrated by themap which spans the 50 largest metropolitan areas in the United States [3]. The basiclinks’ costs in the graph are equal to the physical distance between the nodes they con-nect, links spanning greater distance cost more. We set the source node in this map to

∗For convenient, instead of ignoring the source as a place for transcoding, one can assume that conversion atthe source is very expensive and thus it does not pay to transcode at the root.

434 Session Nine QoS Composition and Adaptation

Figure 3: The U.S.A as realistic platform for the TPM algorithm

be Washington DC and all nodes (Washington included) are clients. We consider a for-mat conversion scheme which deals with a realistic compression conversions that cantake place with a MPEG-4 media stream. This conversion scheme is mentioned in [6]and contains five different profiles (formats) of MPEG-4. The conversions’ ratio that arementioned are 1, 1, 0.5, 0.16, 0.032 and the converting graphs representing a compressioncapability only, meaning, f1 → f2 → f3 → f4 → f5. We assume in this simulation thatequal amount of nodes (metropolitan areas) receive the media stream in a different format(Each format in the system has 10 nodes representing clients demanding that specific for-mat). The transcodings’ costs from one format to another are chosen randomly for everygraph node.In this set of simulations we want to demonstrate the benefit of allowing an increasingamount of nodes to host transcoders. In each run of the simulation we added additional 5transcoders and then checked the cost of our solution. In the map presented, the triangularnodes are the ones capable of transcoding at a certain round of the simulation.

In Figure 4 we present a table containing the results of the simulation. It is clear fromthe table that when more transcoders are available the cheaper the final result becomes.This analysis, that ignores issues like the ratio between conversions’ cost and connec-tion cost, is obvious since our algorithm always look for the shortest path connecting thesource to each layer in the MLMG. As more transcoders are opened the more optionsthe algorithm has for paths searching. There are, however, situations in which despite theopening of more transcoders the TPM’s solution’s cost doesn’t decrease. This effect ofdiminishing return indicates the point where enough transcoders were already placed.

Next we would like to compare the performance of our BF algorithm and the two othersimple heuristics for solving the TPM problem. The first heuristic is format conversion atthe clients. Meaning, the media origin sends the media stream in the original format f1,and each client transcode it to suit its needed format. The second heuristic is transcodingat the source. The source creates copies of the media stream in all formats and multicasteach media format to all compatible clients. We compare these two heuristics to our BFalgorithm which can choose transformation at intermediate nodes in the network (our

435Efficient Management of Transcoding and Multicasting Multimedia Streams

Figure 4: TPM algorithm as a function of the amount of open transcoders

Figure 5: Evaluating our TPM algorithm

algorithm examines also the other two options). The comparison of the three methodsis demonstrated by the ratio between each of the two simple heuristics solutions’ costsand our BF algorithm’s cost. The simulation was running on a graph representing anISP’s (Internet Service Provider) network. We have created such a graph using the BRITE

tool [18] over the Waxman’s model [24]. Our graph included 250 nodes and exactly 1250edges.

Figure 5a shows the performance of our algorithm as a function of the ratio betweenthe average communication cost and the average conversion cost. The formats’ conversionthat was used in that simulation was the previous MPEG-4 converting scheme (a com-pression conversion scheme with the following compression ratios 1, 1, 0.5, 0.16, 0.032).Figure 5b presents our algorithm performance as a function of the compression formu-lated by the system’s formats. For example, a 5% compression represents the followingformats: 1, 0.95, 0.9, 0.857, 0.81.... (each format compresses the former format by 5%), a10% compression is represented by the following vector: 1, 0.9, 0.81, 0.73, 0.66... etc...

The graphs in Figure 5 reflect the advantage of our BF algorithm. When increasingthe average cost of conversions, as presented in 5a, our BF algorithm preserves its relativecost, whereas the other two trivial solutions suffer from an increase in cost. Thus, the ratio

436 Session Nine QoS Composition and Adaptation

between the simple heuristics’ costs and our algorithm’s costs increases. On the average,transcoding at the clients costs 15 times more than our BF heuristic, and transcoding at thesource costs more than twice our algorithm. Graph 5b demonstrates our algorithm’s ad-vantage when dealing with large compressions. Although the other two solutions showedno decrease in cost, as compression increases, our algorithm does. As a consequence, theratio between the two heuristics and our algorithm increases. On the average, transcodingat the clients costs 12 times more than our algorithm, and transcoding at the source costsmore than twice the cost of our algorithm.

6. Conclusion and Future Work

In this paper we addressed the question of efficient management of transcoding and mul-ticasting multimedia streams. We identified the need for formats’ conversion when mul-ticasting a media stream in a heterogenous environment. Furthermore, we have examinedthe option of transcoding the streams at intermediate network elements. This option iscrucial especially when considering peer to peer applications. We showed, using simula-tions, that our developed scheme for intermediate transcoding has a better performancein terms of cost than the commonly used solutions for the problem. The results presentedin this paper are only a first step for many interesting problems. A basic extension of ourinvestigated problem is the case of multiple sources for the multimedia streams. Is therean efficient scheme that can help us place transcoders in such a system without consider-ing each source separately. Another practical question is the adjustment of our problem toa constrained network in which connection links have bounded capacities. In such a net-work links should be used in a stinginess way that does not exceed their capacity. Findinggood algorithms for transcoders’ placement in a constrained network is a very challengingand interesting question for future research.

References[1] Bo Shen, Sung-Ju Lee. Transcoding-Enabled Caching Proxy System for Video Delivery in

Heterogeneous Network Environments. In Proceedings of IASTED IMSA 2002, Kauai, HI,August 2002.

[2] Moses Charikar, Chandra Chekuri, To yat Cheung, Zuo Dai, Ashish Goel, Sudipto Guha, andMing Li. Approximation algorithms for directed steiner problems. In Proceedings of the ninthannual ACM-SIAM symposium on Discrete algorithms, pages 192–200. Society for Industrialand Applied Mathematics, 1998.

[3] S. Choi, J. Turner, and T. Wolf. Configuring sessions in programmable networks. ComputerNetworks, 41(2):269–284, February 2003.

[4] Sumi Choi and Yuval Shavitt. Proxy location problems and their generalizations. 23rd Inter-national Conference on Distributed Computing Systems Workshops, page 898, 2003.

[5] Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introductionto Algorithms, Second Edition. The MIT Press, September 2001.

[6] Itai Dabran, Phillip Klein, and Danny Raz. Efficient management of multimedia attachments.In Proceedings of the 7th international workshop on Management of Multimedia networksand services (MMNS), October 2004.

[7] Markus Eiglsperger and Michael Kaufmann. An approach for mixed upward planarization.

437Efficient Management of Transcoding and Multicasting Multimedia Streams

In Proceedings of the 7th International Workshop on Algorithms and Data Structures, pages352–364. Springer-Verlag, 2001.

[8] Armando Fox and Eric A. Brewer. Reducing www latency and bandwidth requirements viareal-time distillation. Fifth International World Wide Web Conference, pages 1445 – 1456,1996.

[9] Eran Halperin and Robert Krauthgamer. Polylogarithmic inapproximability. In Proceedingsof the thirty-fifth annual ACM symposium on Theory of computing, pages 585–594. ACMPress, 2003.

[10] Richard Han, Pravin Bhagwat, Richard LaMaire, Todd Mummert, Veronique Perret, and JimRubas. Dynamic adaptation in an image transcoding proxy for mobile web browsing. IEEEMobile Communications Magazine, pages 8–17, 1998.

[11] Hari Kalva, Anthony Vetro and Huifang Sun. Performance Optimization of an MPEG-2 toMPEG-4 Video Transcoder . SPIE Conference on VLSI Circuits and Systems, Vol. 5117, pp.341-350, May 2003.

[12] D. S. Hochbaum. Approximation Algorithms for NP-hard problems. PWS Publishing Com-pany, Boston, MA, 1997.

[13] Sugih Jamin, Cheng Jin, Anthony R. Kurc, Danny Raz, and Yuval Shavitt. Idmaps: A globalinternet host distance estimation service. IEEE/ACM Trans. on Networking, Oct. 2001.

[14] Samir Khuller and An Zhu. The general steiner tree-star problem. Inf. Process. Lett.,84(4):215–220, 2002.

[15] P. Krishnan, D. Raz, and Y. Shavitt. The cache location problem. IEEE/ACM Transactionson Networking (TON), 8:568 – 582, 2000.

[16] Keqiu Li and Hong Shen. Transcoding proxy placement in en-route web caching. Communi-cation Networks and Services Research Conference (CNSR 2004), 2004.

[17] Huadong Ma and Kang G. Shin. Multicast video-on-demand services. SIGCOMM Comput.Commun. Rev., 32(1):31–43, 2002.

[18] Alberto Medina, Anukool Lakhina, Ibrahim Matta, and John Byers. Brite: An approach touniversal topology generation. In Proceedings of the Ninth International Symposium in Mod-eling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS’01),page 346. IEEE Computer Society, 2001.

[19] Sangheon Pack, EunKyung Paik, and Yanghee Choi. Design of sip transformation server forefficient media negotiation. In Proceedings of SPIE (ITCOM 2001), volume 4522, 2001.

[20] Joseph C. Pasquale, George C. Polyzos, and George Xylomenos. The multimedia multicastingproblem. Multimedia Syst., 6(1):43–59, 1998.

[21] G. Robins and A. Zelikovsky. Improved steiner tree approximation in graphs. In Proceedingsof ACM/SIAM Symposium on Discrete Algorithms (SODA2000), pages 770–779. ACM-SIAM,2000.

[22] Dan Rubenstein, Nicholas F. Maxemchuk, and David Shur. A centralized, tree-based approachto network repair service for multicast streaming media. In Proceedings of the 10th Interna-tional Workshop on Network and Operating System Support for Digital Audio and Video, June26-28 2000.

[23] Zabele S., Dorsch M., Ge Z., Ji P., Keaton M., Kurose J., Shapiro J., and Towsley D. Sands:Specialized active networking for distributed simulation. May 2002.

[24] B. Waxman. Routing of multipoint connections. IEEE J. Select. Areas Commun., December1988.

[25] Leonid Zosin and Samir Khuller. On directed steiner trees. In Proceedings of the thirteenthannual ACM-SIAM symposium on Discrete algorithms, pages 59–63. Society for Industrialand Applied Mathematics, 2002.

438 Session Nine QoS Composition and Adaptation