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Exact Algorithms for Allocation Problems

  • Sundar Annamalai
  • N. S. Narayanaswamy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10823)

Abstract

We design new exact exponential time algorithms for the well known NP-hard allocation problems- Makespan minimization, the Santa Claus problem (with and without capacity constraints) and the Bin packing problem. These problems are very well-studied in the paradigm of approximation algorithms. However the best known exact, exponential-time algorithms for all of the above problems has complexity of \(O^*(3^m)\) [6], where m is the number of jobs except for Bin Packing which has a \(O^*(2^m)\) inclusion exclusion based algorithm (where m is the number of items) [8]. We introduce a new dynamic programming formulation which helps solve Makespan minimization and Santa Claus problem more efficiently in \(O^*(2^m)\) time and gives a completely different approach with the same time complexity in case of Bin Packing. In addition, Jansen et al. [6] showed that unless the ETH (exponential time hypothesis) is false, there is no exact algorithm that runs in time \(2^{o(m)}\).

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringIndian Institute of TechnologyMadrasIndia

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