Lecture 1

Jonathan Mares

January 21, 2015

1 Introduction

Professor Tardos gives an overview of some algorithmic paradigms.

2 Interval scheduling

Application: ReservationsInput: list of requestssi = start of request i, fi = finish time request i, vi = value of iGoals:

take max requests

maximize total value

3 Matching Problem

Boys to girlsInput: two lists of items, list of possible matches?Goals:

match maximum number of pairs

maximum value

allow collision

satisfy preferences

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4 Independent set

Input: list of items to select from, list of conflicting pairsHowever, certain pairs of items have conflictsGoal: select as many as possible avoiding conflictsWe will prove that this type of problem is hardClaim: harder than interval schedulingProof: item = requesttwo conflict if intervals overlapClaim: hard than matchingthe items are possible pairs, conflict is when there are collisions

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