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Approximation of dense-n/2-subgraph and table compression problems-subgraph and table compression problems

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Abstract

We develop improved approximation algorithms for two NP-hard problems: the dense-n/2-subgraph and table compression. Based on SDP relaxation and advanced rounding techniques, we first propose 0.5982 and 0.5970-approximation algorithms respectively for the dense-2-subgraph problem (DSP) and the table compression problem (TCP). Then we improve these bounds to 0.6243 and 0.6708 respectively for DSP and TCP by adding triangle inequalities to strengthen the SDP relaxation. The results for TCP beat the 0.5 bound of a simple greedy algorithm on this problem, and hence answer an open question of Anderson in an affirmative way.

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Authors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100022, Beijing, China

    Dachuan Xu

  2. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100080, Beijing, China

    Jiye Han

  3. Faculty of Administration, University of New Brunswick, P.O. Box 4400, E3B 5A3, Fredericton, NB, Canada

    Donglei Du

Authors
  1. Dachuan Xu
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  2. Jiye Han
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  3. Donglei Du
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Correspondence to Dachuan Xu.

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Xu, D., Han, J. & Du, D. Approximation of dense-n/2-subgraph and table compression problems-subgraph and table compression problems. Sci. China Ser. A-Math. 48, 1223–1233 (2005). https://doi.org/10.1360/04ys0167

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  • DOI: https://doi.org/10.1360/04ys0167

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