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Improved parallel approximation of a class of integer programming problems

  • Session 14: Parallel Algorithms
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1099))

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Abstract

We present a method to derandomize RNC algorithms, converting them to NC algorithms. Using it, we show how to approximate a class of NP-hard integer programming problems in NC, to within factors better than the current-best NC algorithms (of Berger & Rompel and Motwani, Naor & Naor); in some cases, the approximation factors are as good as the best-known sequential algorithms, due to Raghavan. This class includes problems such as global wire-routing in VLSI gate arrays. Also for a subfamily of the “packing” integer programs, we provide the first NC approximation algorithms; this includes problems such as maximum matchings in hypergraphs, and generalizations. The key to the utility of our method is that it involves sums of superpolynomially many terms, which can however be computed in NC; this superpolynomiality is the bottleneck for some earlier approaches.

Work was done in part while visiting the Institute for Advanced study, School of Mathematics, Princeton, NJ 08540, USA, supported in part by the Sloan Foundation, grant No. 93-6-6 and by the Fund for Basic Research administered by the Israel Academy of Sciences.

Work done in part at the National University of Singapore, at DIMACS (supported in part by NSF-STC91-19999 and by support from the N.J. Commission on Science and Technology), and at the Institute for Advanced Study, Princeton (supported in part by grant 93-6-6 of the Alfred P. Sloan Foundation).

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    Noga Alon

  2. Dept. of Information Systems & Computer Science, National University of Singapore, 119260, Singapore, Republic of Singapore

    Aravind Srinivasan

Authors
  1. Noga Alon
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  2. Aravind Srinivasan
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Editor information

Friedhelm Meyer Burkhard Monien

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© 1996 Springer-Verlag Berlin Heidelberg

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Alon, N., Srinivasan, A. (1996). Improved parallel approximation of a class of integer programming problems. In: Meyer, F., Monien, B. (eds) Automata, Languages and Programming. ICALP 1996. Lecture Notes in Computer Science, vol 1099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61440-0_159

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  • DOI: https://doi.org/10.1007/3-540-61440-0_159

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61440-1

  • Online ISBN: 978-3-540-68580-7

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