Finding, minimizing, and counting weighted subgraphs

d Abstract] Virginia Vassilevska School of Mathematics Institute for Advanced Study Princeton, NJ 08540 USA [e-mail] Ryan Williams School of Mathematics Institute for Advanced Study Princeton, NJ 08540 USA [e-mail] For a pattern graph H on k nodes, we consider the problems of finding and counting the number of (not necessarily induced) copies of H in a given large graph G on n nodes, as well as finding minimum weight copies in both node-weighted and edge-weighted graphs. Our results include: ? The number of copies of an H with an independent set of size s can be computed exactly in O (2s nk-s+3 ) time. A minimum weight copy of such an H (with arbitrary real weights on nodes and edges) can be found in O(4s+o(s) nk-s+3 ) time. (The O notation omits poly(k) factors.) These algorithms rely on fast algorithms for computing the permanent of a k ? n matrix, over rings and semirings. ? The number of copies of any H having minimum (or maximum) node-weight (with arbitrary re...

• Type: Conference
• Year: 2009
• Where: STOC
• Authors: Virginia Vassilevska, Ryan Williams
• Keywords: Advanced Study Princeton, Algorithms, Arbitrary Real Weights, Minimum Weight Copies, STOC 2009