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- W2008238596 abstract "We present an algorithm with runtime O(k(2k)n3 * m) for the following NP-complete problem: Given an arbitrary graph G on n vertices and m edges, can we obtain an interval graph by adding at most k new edges to G? This resolves the long-standing open question, first posed by Kaplan, Shamir and Tarjan, of whether this problem could be solved in time f(k) * n(O(1)).The problem has applications in Physical Mapping of DNA and in Profile Minimization for Sparse Matrix Computations. For the first application, our results show tractability for the case of a small number k of false negative errors, and for the second, a small number k of zero elements in the envelope.Our algorithm performs bounded search among possible ways of adding edges to a graph to obtain an interval graph, and combines this with a greedy algorithm when graphs of a certain structure are reached by the search. The presented result is surprising, as it was not believed that a bounded search tree algorithm would suffice to answer the open question affirmatively." @default.
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- W2008238596 date "2007-06-11" @default.
- W2008238596 modified "2023-09-25" @default.
- W2008238596 title "Interval completion with few edges" @default.
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- W2008238596 doi "https://doi.org/10.1145/1250790.1250847" @default.
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