Generalized Assignment of Time-Sensitive Item Groups

Authors Kanthi Sarpatwar, Baruch Schieber, Hadas Shachnai

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Kanthi Sarpatwar
  • IBM Research, Yorktown Heights, NY, USA
Baruch Schieber
  • IBM Research, Yorktown Heights, NY, USA
Hadas Shachnai
  • Computer Science Department, Technion, Haifa, Israel

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Kanthi Sarpatwar, Baruch Schieber, and Hadas Shachnai. Generalized Assignment of Time-Sensitive Item Groups. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We study the generalized assignment problem with time-sensitive item groups (chi-AGAP). It has central applications in advertisement placement on the Internet, and in virtual network embedding in Cloud data centers. We are given a set of items, partitioned into n groups, and a set of T identical bins (or, time-slots). Each group 1 <= j <= n has a time-window chi_j = [r_j, d_j]subseteq [T] in which it can be packed. Each item i in group j has a size s_i>0 and a non-negative utility u_{it} when packed into bin t in chi_j. A bin can accommodate at most one item from each group and the total size of the items in a bin cannot exceed its capacity. The goal is to find a feasible packing of a subset of the items in the bins such that the total utility from groups that are completely packed is maximized. Our main result is an Omega(1)-approximation algorithm for chi-AGAP. Our approximation technique relies on a non-trivial rounding of a configuration LP, which can be adapted to other common scenarios of resource allocation in Cloud data centers.

Subject Classification

ACM Subject Classification
  • Theory of computation → Packing and covering problems
  • Approximation Algorithms
  • Packing and Covering problems
  • Generalized Assignment problem


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