Randomized approximation algorithms for set multicover problems with applications to reverse engineering of protein and gene networks

Piotr Berman, Bhaskar DasGupta, Eduardo Sontag

    Research output: Contribution to journalArticle

    24 Citations (Scopus)

    Abstract

    In this paper we investigate the computational complexity of a combinatorial problem that arises in the reverse engineering of protein and gene networks. Our contributions are as follows:•We abstract a combinatorial version of the problem and observe that this is "equivalent" to the set multicover problem when the "coverage" factor k is a function of the number of elements n of the universe. An important special case for our application is the case in which k = n - 1.•We observe that the standard greedy algorithm produces an approximation ratio of Ω (log n) even if k is "large" i.e k = n - c for some constant c > 0.•Let 1 < a < n denote the maximum number of elements in any given set in our set multicover problem. Then, we show that a non-trivial analysis of a simple randomized polynomial-time approximation algorithm for this problem yields an expected approximation ratio E [r (a, k)] that is an increasing function of a / k. The behavior of E [r (a, k)] is roughly as follows: it is about ln (a / k) when a / k is at least about e2 ≈ 7.39, and for smaller values of a / k it decreases towards 1 as a linear function of sqrt(a / k) with lima / k → 0 E [r (a, k)] = 1. Our randomized algorithm is a cascade of a deterministic and a randomized rounding step parameterized by a quantity β followed by a greedy solution for the remaining problem. We also comment about the impossibility of a significantly faster convergence of E [r (a, k)] towards 1 for any polynomial-time approximation algorithm.

    Original languageEnglish (US)
    Pages (from-to)733-749
    Number of pages17
    JournalDiscrete Applied Mathematics
    Volume155
    Issue number6-7
    DOIs
    StatePublished - Apr 1 2007

    Fingerprint

    Gene Networks
    Reverse engineering
    Reverse Engineering
    Approximation algorithms
    Randomized Algorithms
    Approximation Algorithms
    Genes
    Proteins
    Protein
    Polynomials
    Polynomial-time Algorithm
    Randomized Rounding
    Computational complexity
    Increasing Functions
    Combinatorial Problems
    Approximation
    Greedy Algorithm
    Linear Function
    Cascade
    Computational Complexity

    All Science Journal Classification (ASJC) codes

    • Discrete Mathematics and Combinatorics
    • Applied Mathematics

    Cite this

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    Randomized approximation algorithms for set multicover problems with applications to reverse engineering of protein and gene networks. / Berman, Piotr; DasGupta, Bhaskar; Sontag, Eduardo.

    In: Discrete Applied Mathematics, Vol. 155, No. 6-7, 01.04.2007, p. 733-749.

    Research output: Contribution to journalArticle

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