TY - GEN

T1 - An efficient partitioning oracle for bounded-treewidth graphs

AU - Edelman, Alan

AU - Hassidim, Avinatan

AU - Nguyen, Huy N.

AU - Onak, Krzysztof

N1 - Place of conference:USA

PY - 2011

Y1 - 2011

N2 - Partitioning oracles were introduced by Hassidim et al. (FOCS 2009) as a generic tool for constant-time algorithms. For any ε > 0, a partitioning oracle provides query access to a fixed partition of the input bounded-degree minor-free graph, in which every component has size poly(1/ε), and the number of edges removed is at most εn, where n is the number of vertices in the graph. However, the oracle of Hassidim et al. makes an exponential number of queries to the input graph to answer every query about the partition. In this paper, we construct an efficient partitioning oracle for graphs with constant treewidth. The oracle makes only O(poly(1/ε)) queries to the input graph to answer each query about the partition. Examples of bounded-treewidth graph classes include k-outerplanar graphs for fixed k, series-parallel graphs, cactus graphs, and pseudoforests. Our oracle yields poly(1/ε)-time property testing algorithms for membership in these classes of graphs. Another application of the oracle is a poly(1/ε)-time algorithm that approximates the maximum matching size, the minimum vertex cover size, and the minimum dominating set size up to an additive εn in graphs with bounded treewidth. Finally, the oracle can be used to test in poly(1/ε) time whether the input bounded-treewidth graph is k-colorable or perfect.

AB - Partitioning oracles were introduced by Hassidim et al. (FOCS 2009) as a generic tool for constant-time algorithms. For any ε > 0, a partitioning oracle provides query access to a fixed partition of the input bounded-degree minor-free graph, in which every component has size poly(1/ε), and the number of edges removed is at most εn, where n is the number of vertices in the graph. However, the oracle of Hassidim et al. makes an exponential number of queries to the input graph to answer every query about the partition. In this paper, we construct an efficient partitioning oracle for graphs with constant treewidth. The oracle makes only O(poly(1/ε)) queries to the input graph to answer each query about the partition. Examples of bounded-treewidth graph classes include k-outerplanar graphs for fixed k, series-parallel graphs, cactus graphs, and pseudoforests. Our oracle yields poly(1/ε)-time property testing algorithms for membership in these classes of graphs. Another application of the oracle is a poly(1/ε)-time algorithm that approximates the maximum matching size, the minimum vertex cover size, and the minimum dominating set size up to an additive εn in graphs with bounded treewidth. Finally, the oracle can be used to test in poly(1/ε) time whether the input bounded-treewidth graph is k-colorable or perfect.

UR - http://www.scopus.com/inward/record.url?scp=80052343116&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-22935-0_45

DO - 10.1007/978-3-642-22935-0_45

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AN - SCOPUS:80052343116

SN - 9783642229343

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 530

EP - 541

BT - Approximation, Randomization, and Combinatorial Optimization

T2 - 14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011

Y2 - 17 August 2011 through 19 August 2011

ER -