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Surface Split Decompositions and Subgraph Isomorphism in Graphs on Surfaces
"... The Subgraph Isomorphism problem asks, given a host graph G on n vertices and a pattern graph P on k vertices, whether G contains a subgraph isomorphic to P. The restriction of this problem to planar graphs has often been considered. After a sequence of improvements, the current best algorithm for p ..."
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The Subgraph Isomorphism problem asks, given a host graph G on n vertices and a pattern graph P on k vertices, whether G contains a subgraph isomorphic to P. The restriction of this problem to planar graphs has often been considered. After a sequence of improvements, the current best algorithm for planar graphs is a linear time algorithm by Dorn (STACS ’10), with complexity 2O(k) · O(n). We generalize this result, by giving an algorithm of the same complexity for graphs that can be embedded in surfaces of bounded genus. In addition, we simplify the algorithm and analysis. The key to these improvements is the introduction of surface split decompositions for bounded genus graphs, which generalize sphere cut decompositions for planar graphs. We extend the algorithm for the problem of counting and generating all subgraphs isomorphic to P, even for the case where P is disconnected. This answers an open question by Eppstein (JGAA’99).
Bidimensionality Theory and Algorithmic Graph Minor Theory  Lecture Notes for MohammadTaghi Hajiaghayi’s Tutorial
, 2007
"... Dealing with Hard Graph Problems Many graph problems cannot be computed in polynomial time unless P = NP, which most computer scientists and mathematicians doubt. Examples are the Traveling Salesman Problem (TSP), vertex cover, and dominating set. TSP is to find a Hamiltonian cycle with the least we ..."
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Dealing with Hard Graph Problems Many graph problems cannot be computed in polynomial time unless P = NP, which most computer scientists and mathematicians doubt. Examples are the Traveling Salesman Problem (TSP), vertex cover, and dominating set. TSP is to find a Hamiltonian cycle with the least weight in a complete weighted graph.
Welcome
"... Welcome to the latest issue of the Parameterized Complexity Newsletter. Our aim is to be provocative and informative, suggesting new problems while keeping the community abreast of the rapidly expanding list of applications and techniques. The world records of FPT races (as we know them) are summari ..."
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Welcome to the latest issue of the Parameterized Complexity Newsletter. Our aim is to be provocative and informative, suggesting new problems while keeping the community abreast of the rapidly expanding list of applications and techniques. The world records of FPT races (as we know them) are summarized. The newsletter publishes exercises for classes, as well as new research ideas. There have been an increasing number of parameterized complexity papers presented at conferences this past year. We are all proud of the smart researchers doing such excellent work and I have tried to list some of them in this newsletter. I apologize for those missed. Some nonparameterized papers have also probably been listed. Contributions or requests may be sent to my email address: