Lecture 8 Objectives
• Material from Chapter 9
• More complete introduction of MPI functions
• Show how to implement manager-worker programs
• Parallel Algorithms for Document Classification
• Parallel Algorithms for Clustering
Outline
• Introduce MPI functionality• Introduce problem• Parallel algorithm design• Creating communicators• Non-blocking communications• Implementation• Pipelining• Clustering
Implementation of a Very Simple Document Classifier
• Manager/Worker Design Strategy
• Manager description (create initial tasks and communicate to/from workers)
• Worker description (receive tasks, enter an alternating communication from/to master and computation
Structure of Main program:Manager/Worker Paradigm
MPI_Init (&argc, &argv); // what is my rank?
MPI_Comm_rank(MPI_COMM_WORLD, &myrank);// how many processors are there?
MPI_Comm_size(MPI_COMM_WORLD, &p); if (myid == 0)
Manager(p); else
Worker(myid, p); MPI_Barrier(MPI_COMM_WORLD);MPI_Finalize();return(0);
More MPI functions
• MPI_Abort
• MPI_Comm_split
• MPI_Isend, MPI_Irecv, MPI_Wait
• MPI_Probe
• MPI_Get_count
• MPI_Testsome
MPI_Abort
• A “quick and dirty” way for one process to terminate all processes in a specified communicator
• Example use: If manager cannot allocate memory needed to store document profile vectors
int MPI_Abort ( MPI_Comm comm, /* Communicator */ int error_code)/* Value returned to calling environment */
Creating a Workers-only Communicator
• To support workers-only broadcast, need workers-only communicator
• Can use MPI_Comm_split
• Excluded processes (e.g., Manager) passes MPI_UNDEFINED as the value of split_key, meaning it will not be part of any new communicator
Workers-only Communicator
int id;MPI_Comm worker_comm;
...
if (!id) /* Manager */ MPI_Comm_split (MPI_COMM_WORLD, MPI_UNDEFINED, id, &worker_comm);
else /* Worker */ MPI_Comm_split (MPI_COMM_WORLD, 0, id, &worker_comm);
Nonblocking Send / Receive
• MPI_Isend, MPI_Irecv initiate operation• MPI_Wait blocks until operation complete• Calls can be made early
– MPI_Isend as soon as value(s) assigned– MPI_Irecv as soon as buffer available
• Can eliminate a message copying step• Allows communication / computation overlap
Function MPI_Isend
int MPI_Isend ( void *buffer, int cnt, MPI_Datatype dtype, int dest, int tag, MPI_Comm comm, MPI_Request *handle)
Pointer to object that identifiescommunication operation
Function MPI_Irecv
int MPI_Irecv ( void *buffer, int cnt, MPI_Datatype dtype, int src, int tag, MPI_Comm comm, MPI_Request *handle)
Pointer to object that identifiescommunication operation
Function MPI_Wait
int MPI_Wait (
MPI_Request *handle,
MPI_Status *status
)
Blocks until operation associated with pointer handle completes.
status points to object containing info on received message
Receiving Problem
• Worker does not know length of message it will receive
• Example, the length of File Path Name
• Alternatives– Allocate huge buffer– Check length of incoming message, then
allocate buffer
• We’ll take the second alternative
Function MPI_Probe
int MPI_Probe (
int src, int tag, MPI_Comm comm, MPI_Status *status)
Blocks until message is available to be received from process with rank src with message tag tag; status pointer gives infoon message size.
Function MPI_Get_count
int MPI_Get_count ( MPI_Status *status, MPI_Datatype dtype, int *cnt)
cnt returns the number of elements in message
MPI_Testsome
• Often need to check whether one or more messages have arrived
• Manager posts a nonblocking receive to each worker process
• Builds an array of handles or request objects• Testsome allows manager to determine how
many messages have arrived
Function MPI_Testsome
int MPI_Testsome ( int in_cnt, /* IN - Number of nonblocking receives to check */
MPI_Request *handlearray, /* IN - Handles of pending receives */
int *out_cnt, /* OUT - Number of completed communications */
int *index_array, /* OUT - Indices of completed communications */
MPI_Status *status_array) /* OUT - Status records for completed comms */
Document Classification Problem
• Search directories, subdirectories for documents (look for .html, .txt, .tex, etc.)
• Using a dictionary of key words, create a profile vector for each document
• Store profile vectors
Data Dependence Graph (1)
Partitioning and Communication
• Most time spent reading documents and generating profile vectors
• Create two primitive tasks for each document
Data Dependence Graph (2)
Agglomeration and Mapping
• Number of tasks not known at compile time
• Tasks do not communicate with each other
• Time needed to perform tasks varies widely
• Strategy: map tasks to processes at run time
Manager/worker-style Algorithm
1. Task/Functional Partitioning2. Domain/Data Partitioning
Roles of Manager and Workers
Manager Pseudocode
Identify documentsReceive dictionary size from worker 0Allocate matrix to store document vectorsrepeat
Receive message from workerif message contains document vector
Store document vectorendifif documents remain then Send worker file
nameelse Send worker termination messageendif
until all workers terminatedWrite document vectors to file
Worker Pseudocode
Send first request for work to managerif worker 0 then
Read dictionary from fileendifBroadcast dictionary among workersBuild hash table from dictionaryif worker 0 then
Send dictionary size to managerendifrepeat
Receive file name from managerif file name is NULL then terminate endifRead document, generate document vectorSend document vector to manager
forever
Task/Channel Graph
Enhancements
• Finding middle ground between pre-allocation and one-at-a-time allocation of file paths
• Pipelining of document processing
Allocation Alternatives
Documents Allocated per Requestn/p
Load imbalance
1
Excessivecommunicationoverhead
Time
Pipelining
Time Savings through Pipelining
Pipelined Manager Pseudocode
a 0 {assigned jobs}j 0 {available jobs}w 0 {workers waiting for assignment}repeat
if (j > 0) and (w > 0) thenassign job to workerj j – 1; w w – 1; a a + 1
elseif (j > 0) thenhandle an incoming message from workersincrement w
elseget another jobincrement j
endifuntil (a = n) and (w = p)
Summary
• Manager/worker paradigm– Dynamic number of tasks– Variable task lengths– No communications between tasks
• New tools for “kit”– Create manager/worker program– Create workers-only communicator– Non-blocking send/receive– Testing for completed communications
• Next Step: Cluster Profile Vectors
K-Means Clustering
• Assumes documents are real-valued vectors. • Assumes distance function on vector pairs• Clusters based on centroids (aka the center of gravity or
mean) of points in a cluster, c:
• Reassignment of instances to clusters is based on distance of vector to the current cluster centroids.
– (Or one can equivalently phrase it in terms of similarities)
cx
xc
||
1(c)μ
K-Means Algorithm
Let d be the distance measure between instances.Select k random instances {s1, s2,… sk} as seeds.Until clustering converges or other stopping criterion: For each instance xi: Assign xi to the cluster cj such that d(xi, sj) is minimal. // Now Update the seeds to the centroid of each cluster) For each cluster cj
sj = (cj)
K Means Example(K=2)
Pick seeds
Reassign clusters
Compute centroids
xx
Reassign clusters
xx xx Compute centroids
Reassign clusters
Converged!
Termination conditions
• Desire that docs in a cluster are unchanged
• Several possibilities, e.g.,– A fixed number of iterations.– Doc partition unchanged.– Centroid positions don’t change.– We’ll choose termination when only small
fraction change (threshold value)
• Quiz:– Describe Manager/Worker pseudo-code that
implements the K-means algorithm in parallel– What data partitioning for parallelism?– How are cluster centers updated and
distributed?
Hints
– objects to be clustered are evenly partitioned among all processes
– cluster centers are replicated– Global-sum reduction on cluster centers is
performed at the end of each iteration to generate the new cluster centers.
– Use MPI_Bcast and MPI_Allreduce