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Faster FPT Algorithm for Graph Isomorphism Parameterized by Eigenvalue Multiplicity [article]

Vikraman Arvind, Gaurav Rattan
2014 arXiv   pre-print
We give a O^*(k^O(k)) time isomorphism testing algorithm for graphs of eigenvalue multiplicity bounded by k which improves on the previous best running time bound of O^*(2^O(k^2/ k)).  ...  We thank Saket Saurabh for suggesting the problem of obtaining a faster isomorphism algorithm for graphs of bounded eigenvalue multiplicity using the O * (k O(k) ) time algorithm for GGI.  ...  In this paper we obtain a O * (k O(k) ) time isomorphism algorithm for graphs of eigenvalue multiplicity bounded by k.  ... 
arXiv:1408.3510v1 fatcat:r3k5f2ckzrhrdidlzule4oaeqq

Modular counting of subgraphs: Matchings, matching-splittable graphs, and paths [article]

Radu Curticapean, Holger Dell, Thore Husfeldt
2021 arXiv   pre-print
For example, it is known that the parity of the number of k-matchings can be determined in polynomial time by a simple reduction to the determinant.  ...  ]-complete, answering an open question by Björklund, Dell, and Husfeldt (ICALP 2015).  ...  A Turing fpt-reduction may query the oracle multiple times for instances whose parameter is bounded by a function of the input parameter, and combine the query answers in fpt-time to produce the correct  ... 
arXiv:2107.00629v1 fatcat:6ch2zonbobgjdjrrkxdr4cz2je

Parameterized (Modular) Counting and Cayley Graph Expanders [article]

Norbert Peyerimhoff and Marc Roth and Johannes Schmitt and Jakob Stix and Alina Vdovina
2021 arXiv   pre-print
In the course of our investigations we also provide an exhaustive parameterized complexity classification for the problem of counting graph homomorphisms modulo a prime p.  ...  Our main result is an exhaustive and fine-grained complexity classification of #EdgeSub(Φ) for minor-closed properties Φ, closing the missing gap in previous work by Roth, Schmitt and Wellnitz (ICALP 21  ...  The third author was supported by the SNF Early Postdoc.Mobility grant 184245 and thanks the Max Planck Institute for Mathematics in Bonn for its hospitality.  ... 
arXiv:2104.14596v1 fatcat:zzjcjpxyrfdljp2g3hpnwvdxlu

Counting Subgraphs via Homomorphisms

Omid Amini, Fedor V. Fomin, Saket Saurabh
2012 SIAM Journal on Discrete Mathematics  
polynomial, the classical algorithm of Kohn, Gottlieb, Kohn, and Karp for counting Hamiltonian cycles, Ryser's formula for counting perfect matchings of a bipartite graph, and color coding based algorithms  ...  This approach provides new algorithms and unifies several well known results in algorithms and combinatorics including the recent algorithm of Björklund, Husfeldt and Koivisto for computing the chromatic  ...  Acknowledgement Many thanks to László Lovász for answering our questions on graph homomorphisms.  ... 
doi:10.1137/100789403 fatcat:igr4ivf2z5gg3h3zabvnwnfifm

Counting Subgraphs via Homomorphisms [chapter]

Omid Amini, Fedor V. Fomin, Saket Saurabh
2009 Lecture Notes in Computer Science  
polynomial, the classical algorithm of Kohn, Gottlieb, Kohn, and Karp for counting Hamiltonian cycles, Ryser's formula for counting perfect matchings of a bipartite graph, and color coding based algorithms  ...  This approach provides new algorithms and unifies several well known results in algorithms and combinatorics including the recent algorithm of Björklund, Husfeldt and Koivisto for computing the chromatic  ...  Acknowledgement Many thanks to László Lovász for answering our questions on graph homomorphisms.  ... 
doi:10.1007/978-3-642-02927-1_8 fatcat:uw247ph62rbnjeggb2k3ysqq3y

Algorithmic Aspects of Regular Graph Covers [article]

Jiří Fiala, Pavel Klavík, Jan Kratochvíl, Roman Nedela
2017 arXiv   pre-print
Another special case arises for |G| = |H| when it becomes the graph isomorphism problem.  ...  Our main result is an involved FPT algorithm solving RegularCover for planar inputs G in time O^*(2^e(H)/2) where e(H) denotes the number of edges of H.  ...  It also implies a quadratic-time algorithm for AutGroup of planar graphs (which likely can be improved to linear time), faster than the best previous trivial O(n 4 ) algorithm by combining [38, 49] .  ... 
arXiv:1609.03013v2 fatcat:6r7hqzcekzaldlbt2vzq7x2ap4

Reinforcement Learning (Dagstuhl Seminar 13321) The Critical Internet Infrastructure (Dagstuhl Seminar 13322) Coding Theory (Dagstuhl Seminar 13351) Interaction with Information for Visual Reasoning (Dagstuhl Seminar 13352)

Peter Auer, Marcus Hutter, Laurent, Georg Carle, Jochen Schiller, Steve Uhlig, Walter Willinger, Matthias Wählisch, Thore Husfeldt, Ramamohan Paturi, Gregory Sorkin, Ryan Williams (+14 others)
unpublished
We were later joined by Susana: Largely ignored -ICT is needed for bridging these models. Mark: THink of a whirlpool engineer, modern washing machines considers chemicals, mechanical etc. aspects.  ...  We gratefully acknowledge the Dagstuhl staff for helping on all administrative coordination, for their patience, and most importantly for providing an extremely inspiring environment.  ...  the obtained graph is isomorphic to F .  ... 
fatcat:iz3co5xisfejfbnx2t6ptrorfm

50 Algebra in Computational Complexity (Dagstuhl Seminar 14391) Manindra Agrawal, Valentine Kabanets, Thomas Thierauf, and Christopher Umans 85 Privacy and Security in an Age of Surveillance (Dagstuhl Perspectives Workshop

Maria-Florina Balcan, Bodo Manthey, Heiko Röglin, Tim Roughgarden, Artur D'avila Garcez, Marco Gori, Pascal Hitzler, Luís Lamb, Bart Preneel, Phillip Rogaway, Mark Ryan, Peter (+5 others)
unpublished
The results show that the Edge Pushing algorithm can be faster than the currently used algorithms (that compute compressed Hessian matrices via graph coloring) for some problems by one or two orders of  ...  We study the parameterized complexity of the following counting version of subgraph isomorphism: Given a "pattern" graph H and a "host" graph G, count the (not necessarily induced) copies of H in G, that  ...  Faster All-Pairs Shortest Paths Via Circuit Complexity Ryan Williams (Stanford University, US) License Creative Commons BY 3.0 Unported license © Ryan Williams I presented an algorithm for solving the  ... 
fatcat:e5wnf6cuhvc3bceegijgut34zm

Dagstuhl Reports, Volume 8, Issue 10, October 2018, Complete Issue [article]

2019
their contributions and extend special thanks to the moderators of the breakout sessions and the team of Schloss Dagstuhl for helping to make this seminar a success.  ...  Houston, US), Hannes Mühleisen (CWI -Amsterdam, NL), Cagatay Turkay (City -University of London, GB), Frank van Ham (IBM Netherlands -Weert, NL) Acknowledgment The organizers thank all the attendees for  ...  We give faster enumeration algorithms for directed graphs with at most 0.8004n vertices occurring in 2-cycles.  ... 
doi:10.4230/dagrep.8.10 fatcat:q5uhtls46rd3zf4cnl4szgxc7y

LIPIcs, Volume 2, FSTTCS'08, Complete Volume [article]

Ramesh Hariharan, Madhavan Mukund, V Vinay
2013
Acknowledgments Thanks are due to anonymous referees for helpful comments. This work was partially supported by a grant from JSPS, No. 20500002. Acknowledgements.  ...  Arvind, and Meena Mahajan for helpful discussions, and the anonymous referees for helpful comments. Acknowledgement We thank Santosh Vempala for interesting discussions on this problem.  ...  In this paper we fill this gap by initiating parameterized algorithmic study of these problems on structural graphs like planar graphs, graphs of bounded genus and graphs of bounded local treewidth.  ... 
doi:10.4230/lipics.fsttcs.2008 fatcat:byk56drkgzc6dlyzfnfysbydoq