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Chromatic kernel and its applications

Author

Listed:
  • Hu Ding

    (State University of New York at Buffalo)

  • Branislav Stojkovic

    (State University of New York at Buffalo)

  • Zihe Chen

    (State University of New York at Buffalo)

  • Andrew Hughes

    (State University of New York at Buffalo)

  • Lei Xu

    (State University of New York at Buffalo)

  • Andrew Fritz

    (State University of New York at Buffalo)

  • Nitasha Sehgal

    (State University of New York at Buffalo)

  • Ronald Berezney

    (State University of New York at Buffalo)

  • Jinhui Xu

    (State University of New York at Buffalo)

Abstract

In this paper, we study the following Chromatic kernel (CK) problem: given an $$n$$ n -partite graph (called a chromatic correlation graph) $$G=(V,E)$$ G = ( V , E ) with $$V=V_{1}\bigcup \cdots \bigcup V_{n}$$ V = V 1 ⋃ ⋯ ⋃ V n and each partite set $$V_{i}$$ V i containing a constant number $$\lambda $$ λ of vertices, compute a subgraph $$G[V_{CK}]$$ G [ V C K ] of $$G$$ G with exactly one vertex from each partite set and the maximum number of edges or the maximum total edge weight, if $$G$$ G is edge-weighted (among all such subgraphs). CK is a new problem motivated by several applications and no existing algorithm directly solves it. In this paper, we first show that CK is NP-hard even if $$\lambda =2$$ λ = 2 , and cannot be approximated within a factor of $$16/17$$ 16 / 17 unless P = NP. Then, we present a random-sampling-based PTAS for dense CK. As its application, we show that CK can be used to determine the pattern of chromosome associations in the nucleus for a population of cells. We test our approach by using random and real biological data; experimental results suggest that our approach yields near optimal solutions, and significantly outperforms existing approaches.

Suggested Citation

  • Hu Ding & Branislav Stojkovic & Zihe Chen & Andrew Hughes & Lei Xu & Andrew Fritz & Nitasha Sehgal & Ronald Berezney & Jinhui Xu, 2016. "Chromatic kernel and its applications," Journal of Combinatorial Optimization, Springer, vol. 31(3), pages 1298-1315, April.
  • Handle: RePEc:spr:jcomop:v:31:y:2016:i:3:d:10.1007_s10878-014-9824-z
    DOI: 10.1007/s10878-014-9824-z
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    References listed on IDEAS

    as
    1. Lopamudra Mukherjee & Vikas Singh & Jiming Peng & Jinhui Xu & Michael J. Zeitz & Ronald Berezney, 2009. "Generalized median graphs and applications," Journal of Combinatorial Optimization, Springer, vol. 17(1), pages 21-44, January.
    2. Bernard Chazelle & Carl Kingsford & Mona Singh, 2004. "A Semidefinite Programming Approach to Side Chain Positioning with New Rounding Strategies," INFORMS Journal on Computing, INFORMS, vol. 16(4), pages 380-392, November.
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