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Improved Approximation Algorithms for Weighted 2-Path Partitions

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Algorithms - ESA 2015

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9294))

Abstract

We investigate two NP-complete vertex partition problems on edge weighted complete graphs with 3k vertices. The first problem asks to partition the graph into k vertex disjoint paths of length 2 (referred to as 2-paths) such that the total weight of the paths is maximized. We present a cubic time approximation algorithm that computes a 2-path partition whose total weight is at least .5833 of the weight of an optimal partition; improving upon the (.5265 − ε)-approximation algorithm of [26]. Restricting the input graph to have edge weights in {0, 1}, we present a .75 approximation algorithm improving upon the .55-approximation algorithm of [16].

Combining this algorithm with a previously known approximation algorithm for the 3-Set Packing problem, we obtain a .6-approximation algorithm for the problem of partitioning a {0, 1}-edge-weighted graph into k vertex disjoint triangles of maximum total weight. The best known approximation algorithm for general weights achieves an approximation ratio of .5257 [4].

This work is supported by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-09-2-0053, The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation here on.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Graduate Center, City University of New York, New York, USA

    Amotz Bar-Noy, George Rabanca & Ivo Vigan

  2. Department of Computer Science and Applied Mathematics, Weizmann Institute, Rehovot, Israel

    David Peleg

Authors
  1. Amotz Bar-Noy
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  2. David Peleg
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  3. George Rabanca
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  4. Ivo Vigan
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Editor information

Editors and Affiliations

  1. University of Technology, Eindhoven, The Netherlands

    Nikhil Bansal

  2. Sapienza University of Rome, Rome, Italy

    Irene Finocchi

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Bar-Noy, A., Peleg, D., Rabanca, G., Vigan, I. (2015). Improved Approximation Algorithms for Weighted 2-Path Partitions. In: Bansal, N., Finocchi, I. (eds) Algorithms - ESA 2015. Lecture Notes in Computer Science(), vol 9294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48350-3_79

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  • DOI: https://doi.org/10.1007/978-3-662-48350-3_79

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  • Print ISBN: 978-3-662-48349-7

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