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Journal of the ACM (JACM)
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SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Faster Algebraic Algorithms for Path and Packing Problems
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Finding paths of length k in O∗(2k) time
Information Processing Letters
Finding, minimizing, and counting weighted subgraphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Counting Subgraphs via Homomorphisms
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Limits and Applications of Group Algebras for Parameterized Problems
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Balanced families of perfect hash functions and their applications
ACM Transactions on Algorithms (TALG)
Algorithm for finding k-vertex out-trees and its application to k-internal out-branching problem
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Trimmed Moebius Inversion and Graphs of Bounded Degree
Theory of Computing Systems - Special Title: Symposium on Theoretical Aspects of Computer Science; Guest Editors: Susanne Albers, Pascal Weil
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Exact weight subgraphs and the k-sum conjecture
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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In the Subgraph Isomorphism problem we are given two graphs F and G on k and n vertices respectively as an input, and the question is whether there exists a subgraph of G isomorphic to F. We show that if the treewidth of F is at most t, then there is a randomized algorithm for the Subgraph Isomorphism problem running in time O^@?(2^kn^2^t). Our proof is based on a novel construction of an arithmetic circuit of size at most n^O^(^t^) for a new multivariate polynomial, Homomorphism Polynomial, of degree at most k, which in turn is used to solve the Subgraph Isomorphism problem. For the counting version of the Subgraph Isomorphism problem, where the objective is to count the number of distinct subgraphs of G that are isomorphic to F, we give a deterministic algorithm running in time and space O^@?((nk/2)n^2^p) or (nk/2)n^O^(^t^l^o^g^k^). We also give an algorithm running in time O^@?(2^k(nk/2)n^5^p) and taking O^@?(n^p) space. Here p and t denote the pathwidth and the treewidth of F, respectively. Our work improves on the previous results on Subgraph Isomorphism, it also extends and unifies most of the known results on sub-path and sub-tree isomorphisms.