Clique Clustering Yields a PTAS for max-Coloring Interval Graphs

We are given an interval graph G = (V, E) where each interval I ∈ V has a weight wI ∈ R+. The goal is to color the intervals V with an arbitrary number of color classes C1, C2, . . . , Ck such that k i=1 maxI∈Ci wI is minimized. This problem, called max-coloring interval graphs, contains the classical problem of coloring interval graphs as a special case for uniform weights, and it arises in many practical scenarios such as memory management. Pemmaraju, Raman, and Varadarajan showed that max-coloring interval graphs is NP-hard (SODA’04) and presented a 2-approximation algorithm. Closing a gap which has been open for years, we settle the approximation complexity of this problem by giving a polynomial-time approximation scheme (PTAS), that is, we show that there is an (1 + )-approximation algorithm for any > 0. Besides using standard preprocessing techniques such as geometric rounding and shifting, our main building block is a general technique for trading the overlap structu...

• Type: Journal
• Year: 2011
• Where: ICALP
• Authors: Tim Nonner
• Keywords: ICALP 2011, Interval Graph, Interval Graphs, Polynomial Time Approximation, Programming Languages