TY - GEN

T1 - An exponential time 2-approximation algorithm for bandwidth

AU - Fürer, Martin

AU - Gaspers, Serge

AU - Kasiviswanathan, Shiva Prasad

PY - 2009

Y1 - 2009

N2 - The bandwidth of a graph G on n vertices is the minimum b such that the vertices of G can be labeled from 1 to n such that the labels of every pair of adjacent vertices differ by at most b. In this paper, we present a 2-approximation algorithm for the Bandwidth problem that takes worst-case O(1.9797 n) = O(3 0.6217n) time and uses polynomial space. This improves both the previous best 2- and 3-approximation algorithms of Cygan et al. which have an O*(3 n) and O*(2 n) worst-case time bounds, respectively. Our algorithm is based on constructing bucket decompositions of the input graph. A bucket decomposition partitions the vertex set of a graph into ordered sets (called buckets) of (almost) equal sizes such that all edges are either incident on vertices in the same bucket or on vertices in two consecutive buckets. The idea is to find the smallest bucket size for which there exists a bucket decomposition. The algorithm uses a simple divide-and-conquer strategy along with dynamic programming to achieve this improved time bound.

AB - The bandwidth of a graph G on n vertices is the minimum b such that the vertices of G can be labeled from 1 to n such that the labels of every pair of adjacent vertices differ by at most b. In this paper, we present a 2-approximation algorithm for the Bandwidth problem that takes worst-case O(1.9797 n) = O(3 0.6217n) time and uses polynomial space. This improves both the previous best 2- and 3-approximation algorithms of Cygan et al. which have an O*(3 n) and O*(2 n) worst-case time bounds, respectively. Our algorithm is based on constructing bucket decompositions of the input graph. A bucket decomposition partitions the vertex set of a graph into ordered sets (called buckets) of (almost) equal sizes such that all edges are either incident on vertices in the same bucket or on vertices in two consecutive buckets. The idea is to find the smallest bucket size for which there exists a bucket decomposition. The algorithm uses a simple divide-and-conquer strategy along with dynamic programming to achieve this improved time bound.

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U2 - 10.1007/978-3-642-11269-0_14

DO - 10.1007/978-3-642-11269-0_14

M3 - Conference contribution

AN - SCOPUS:72249097975

SN - 3642112684

SN - 9783642112683

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

SP - 173

EP - 184

BT - Parameterized and Exact Computation - 4th International Workshop, IWPEC 2009, Revised Selected Papers

T2 - 4th International Workshop on Parameterized and Exact Computation, IWPEC 2009

Y2 - 10 September 2009 through 11 September 2009

ER -