PTAS for Densest k-Subgraph in Interval Graphs

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PTAS for Densest k-Subgraph in Interval Graphs
Given an interval graph and integer k, we consider the problem of finding a subgraph of size k with a maximum number of induced edges, called densest k-subgraph problem in interval graphs. It has been shown that this problem is NP-hard even for chordal graphs [17], and there is probably no PTAS for general graphs [12]. However, the exact complexity status for interval graphs is a long-standing open problem [17], and the best known approximation result is a 3-approximation algorithm [16]. We shed light on the approximation complexity of finding a densest k-subgraph in interval graphs by presenting a polynomialtime approximation scheme (PTAS), that is, we show that there is an (1 + )approximation algorithm for any > 0, which is the first such approximation scheme for the densest k-subgraph problem in an important graph class without any further restrictions.
Tim Nonner
Added 29 Mar 2016
Updated 29 Mar 2016
Type Journal
Year 2016
Authors Tim Nonner
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