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Register Loading via Linear Programming

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Algorithms and Data Structures (WADS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6844))

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Abstract

We study the following optimization problem. The input is a number k and a directed graph with a specified “start” vertex, each of whose vertices may have one “memory bank requirement”, an integer. There are k “registers”, labeled 1 …k. A valid solution associates to the vertices with no bank requirement one or more “load instructions” L[b,j], for bank b and register j, such that every directed trail from the start vertex to some vertex with bank requirement c contains a vertex u that has been associated L[c,i] (for some register i ≤ k) and no vertex following u in the trail has been associated an L[b,i], for any bank b. The objective is to minimize the total number of associated load instructions. We give a k(k + 1)-approximation algorithm based on linear programming rounding, with (k + 1) being the best possible unless Vertex Cover has approximation 2 − ε for ε > 0. We also present a O(k logn) approximation, with n being the number of vertices in the input directed graph. Based on the same linear program, another rounding method outputs a valid solution with objective at most 2k times the optimum for k registers, using 2k registers.

Gruia Calinescu is supported in part by NSF grant NeTS-0916743 and Minming Li is supported in part by a grant from Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. CityU117408].

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Author information

Authors and Affiliations

  1. Department of Computer Science, Illinois Institute of Technology, USA

    Gruia Calinescu

  2. Department of Computer Science, City University of Hong Kong, Hong Kong

    Minming Li

Authors
  1. Gruia Calinescu
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  2. Minming Li
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Editor information

Editors and Affiliations

  1. School of Computer Science, Parallel Computing and Bioinformatics Laboratory, Carleton University, VISM Building, Room 6210, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Frank Dehne

  2. Department of Computer Science and Engineering, Polytechnic Institute of New York University, 5 MetroTech Center, 11201, New York, NY, USA

    John Iacono

  3. School of Computer Science, Herzberg Laboratories, Carleton University, Herzberg Building, Room 5350, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Jörg-Rüdiger Sack

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Calinescu, G., Li, M. (2011). Register Loading via Linear Programming. In: Dehne, F., Iacono, J., Sack, JR. (eds) Algorithms and Data Structures. WADS 2011. Lecture Notes in Computer Science, vol 6844. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22300-6_15

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  • DOI: https://doi.org/10.1007/978-3-642-22300-6_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22299-3

  • Online ISBN: 978-3-642-22300-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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