All-or-nothing generalized assignment with application to scheduling advertising campaigns

Ron Adany, Moran Feldman, Elad Haramaty, Rohit Khandekar, Baruch Schieber, Roy Schwartz, Hadas Shachnai, Tami Tamir

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

We study a variant of the generalized assignment problem (gap) which we label all-or-nothing gap ( agap ). We are given a set of items, partitioned into n groups, and a set of m bins. Each item ℓ has size s > 0, and utility aℓj ≥ 0 if packed in bin j. Each bin can accommodate at most one item from each group, and the total size of the items in a bin cannot exceed its capacity. A group of items is satisfied if all of its items are packed. The goal is to find a feasible packing of a subset of the items in the bins such that the total utility from satisfied groups is maximized. We motivate the study of agap by pointing out a central application in scheduling advertising campaigns. Our main result is an O(1)-approximation algorithm for agap instances arising in practice, where each group consists of at most m/2 items. Our algorithm uses a novel reduction of agap to maximizing submodular function subject to a matroid constraint. For agap instances with fixed number of bins, we develop a randomized polynomial time approximation scheme (PTAS), relying on a non-trivial LP relaxation of the problem. We present a (3 + ε)-approximation as well as PTASs for other special cases of agap, where the utility of any item does not depend on the bin in which it is packed. Finally, we derive hardness results for the different variants of agap studied in the paper.

Original languageEnglish (US)
Title of host publicationInteger Programming and Combinatorial Optimization - 16th International Conference, IPCO 2013, Proceedings
Pages13-24
Number of pages12
DOIs
StatePublished - Apr 3 2013
Externally publishedYes
Event16th Conference on Integer Programming and Combinatorial Optimization, IPCO 2013 - Valparaiso, Chile
Duration: Mar 18 2013Mar 20 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7801 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference16th Conference on Integer Programming and Combinatorial Optimization, IPCO 2013
CountryChile
CityValparaiso
Period3/18/133/20/13

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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