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Engineering Fast Almost Optimal Algorithms for Bipartite Graph Matching

Ioannis Panagiotas, Bora Uçar, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
Regular bipartite graphs, where all vertices have the same degree, form another class for which there is an expected O(m + nlog n)-time Las Vegas algorithm.  ...  Random 2-out bipartite graphs, where each vertex chooses two neighbors at random from the other side, form one class for which there is an O(m+nlog n)-time Monte Carlo algorithm.  ...  This modification was not able to find a perfect matching in any of the 39 instances. This led to an increase in the run time, which we deemed too large.  ... 
doi:10.4230/lipics.esa.2020.76 dblp:conf/esa/PanagiotasU20 fatcat:bxkhugrnnbdovibn4la4enrgtm

Exact and Approximation Algorithms for Many-To-Many Point Matching in the Plane [article]

Sayan Bandyapadhyay, Anil Maheshwari, Michiel Smid
2021 arXiv   pre-print
This problem is a restricted version of minimum-weight edge cover in a bipartite graph, and hence can be solved in O(n^3) time.  ...  In a more restricted setting where all the points are on a line, the problem can be solved in O(nlog n) time [Colannino, Damian, Hurtado, Langerman, Meijer, Ramaswami, Souvaine, Toussaint; Graphs Comb.  ...  Acknowledgements We thank Saeed Mehrabi for introducing the many-to-many matching problem to us.  ... 
arXiv:2109.07524v1 fatcat:lsn7krpny5h2ficsofbbxexczy

A Quest for Structure in Complexity

Vikraman Arvind, Meena Mahajan
2017 Bulletin of the European Association for Theoretical Computer Science  
The class SPL contains NLOG and is contained in NC 2 . The perfect matching problem has fascinated complexity theorists for years.  ...  Counting perfect matchings in planar graphs is in P and even NC, whereas in general graphs deciding existence via shallow circuits so far seems to need non-uniformity or quasi-polynomial size.  ... 
dblp:journals/eatcs/ArvindM17 fatcat:axk2knwgpbh6nfdz3bespdpqom

Tight Bounds for Testing Bipartiteness in General Graphs

Tali Kaufman, Michael Krivelevich, Dana Ron
2004 SIAM journal on computing (Print)  
We present an algorithm whose complexity isÕ(min( √ n, n 2 /m)) where m is the number of edges in the graph, and match it with an almost tight lower bound.  ...  In this paper we consider the problem of testing bipartiteness of general graphs.  ...  Consider the following process, denoted by C P , for choosing a random d-regular graph having n vertices (i.e., a perfect matching over a matching table of size n×d).  ... 
doi:10.1137/s0097539703436424 fatcat:rrqzskk4sfeajc4dela2zewjpy

On approximating the d -girth of a graph

David Peleg, Ignasi Sau, Mordechai Shalom
2013 Discrete Applied Mathematics  
algorithms in general graphs, as well as analyzing the case where G is planar.  ...  Keywords: generalized girth, minimum degree, approximation algorithm, hardness of approximation, randomized algorithm, planar graph. ⋆ A preliminary extended abstract of this work appeared in [22] .  ...  We add another copy of E, called F , and d − 1 edge-disjoint perfect matchings on E ∪ F , inducing a bipartite graph with partition classes E and F .  ... 
doi:10.1016/j.dam.2013.04.022 fatcat:5zzhqyjmzjglpeufl2t2fixxtu

On Approximating the d-Girth of a Graph [chapter]

David Peleg, Ignasi Sau, Mordechai Shalom
2011 Lecture Notes in Computer Science  
algorithms in general graphs, as well as analyzing the case where G is planar.  ...  Since then, no new insights have appeared in the literature. Recently, first algorithmic studies of the problem have been carried out [2, 4] .  ...  We add another copy of E, called F , and d − 1 edge-disjoint perfect matchings on E ∪ F , inducing a bipartite graph with partition classes E and F .  ... 
doi:10.1007/978-3-642-18381-2_39 fatcat:24lhgvf2ijakbmzxegjzg7utcy

Bounds on the maximum multiplicity of some common geometric graphs [article]

Adrian Dumitrescu, André Schulz, Adam Sheffer, Csaba D. Tóth
2011 arXiv   pre-print
We give a combinatorial characterization of the longest tours, which leads to an O(nlog n) time algorithm for computing them.  ...  Likewise, we show that both the number of longest non-crossing tours and the number of longest non-crossing perfect matchings can be exponential in n.  ...  Hence a maximum matching on P is a bipartite graph between L and R. To avoid crossings, every edge in such a bipartite graph must connect points in the same copy of S 4 .  ... 
arXiv:1012.5664v2 fatcat:2mjbkstpr5e7ndjdlmlttk6iwa

On the ?log rank?-conjecture in communication complexity

Ran Raz, Boris Spieker
1995 Combinatorica  
We consider the following problem: each of two players gets a perfect matching between two n-element sets of vertices.  ...  Another conclusion from the second result is an Q(7i log log 7 1 ) lower bound for the graph connectivity problem in the non-deterministic case.  ...  Razborov for a very important remark, given in the introduction.  ... 
doi:10.1007/bf01192528 fatcat:gay75pongrfdrox2do2ectkrtq

View-based object recognition using saliency maps

Ali Shokoufandeh, Ivan Marsic, Sven J. Dickinson
1999 Image and Vision Computing  
To compare two saliency map graphs, we introduce two graph similarity algorithms. The first computes the topological similarity between two SMGs, providing a coarse-level matching of two graphs.  ...  The second computes the geometrical similarity between two SMGs, providing a fine-level matching of two graphs.  ...  The time complexity for finding such a matching in a weighted bipartite graph with n vertices is On 2 nlog log n p time, using the scaling algorithm of Gabow et al. [31] .  ... 
doi:10.1016/s0262-8856(98)00124-3 fatcat:e2thtjp2fbf6hdbpfeuagep2wq

Near-Optimal Induced Universal Graphs for Bounded Degree Graphs [article]

Mikkel Abrahamsen, Stephen Alstrup, Jacob Holm, Mathias Bæk Tejs Knudsen, Morten Stöckel
2016 arXiv   pre-print
For the family of all undirected graphs on n vertices Alstrup, Kaplan, Thorup, and Zwick [STOC 2015] give an induced universal graph with O(2^n/2) vertices, matching a lower bound by Moon [Proc.  ...  In addition, we give results for acyclic graphs with max degree 2 and cycle graphs. Our results imply the first labeling schemes that for any D are at most o(n) bits from optimal.  ...  . , i D−1 ∈ [r] Every graph in F is the union of D perfect matchings and therefore has max degree ≤ D. Now fix G ∈ F and let M be a perfect matching G.  ... 
arXiv:1607.04911v2 fatcat:o4pfu5umi5hzpcjm2xu7bswla4

Generation of synthetic sequential benchmark circuits

Michael Hutton, Jonathan Rose, Derek Corneil
1997 Proceedings of the 1997 ACM fifth international symposium on Field-programmable gate arrays - FPGA '97  
By comparing the post-layout properties of the generated circuits with already existing circuits, we demonstrate that the synthetic circuits are m u c h m o r e r ealistic than random graphs with the same  ...  In previous work, we have de ned i m p ortant physical characteristics of combinational circuits.  ...  Acknowledgements: The authors would like t o t h a n k Vaughn Betz for use of vpr.  ... 
doi:10.1145/258305.258333 dblp:conf/fpga/HuttonRC97 fatcat:mog6d4lhbfb4dhfm2yb4m5lyka

Counting truth assignments of formulas of bounded tree-width or clique-width

E. Fischer, J.A. Makowsky, E.V. Ravve
2008 Discrete Applied Mathematics  
In this paper we present an algorithm for GENSAT for formulas of bounded tree-width k which runs in time 4 k (n + n 2 · log 2 (n)), where n is the size of the input.  ...  It is well known, that, given a graph of tree-width k, a k-tree decomposition can be found in polynomial time.  ...  Its running time is O(n 9 log n) and g(k) = 3 3k+O(1) = 2 O(k) .  ... 
doi:10.1016/j.dam.2006.06.020 fatcat:fwer5dkxobbizndf3nrtzpbi5m

Combinatorics, Probability and Computing

Noga Alon, Béla Bollobás, Ingo Wegener
2006 Oberwolfach Reports  
The meeting was dedicated to recent developments in these areas, focusing on the investigation of random graphs and probabilistic methods, on the study of stochastic processes including questions on percolation  ...  One of the exciting phenomena in mathematics in recent years has been the widespread and surprisingly effective use of probabilistic methods in diverse areas.  ...  Next, we find an almost perfect matching M ′′ in H − V (M ′ ) which leaves some set S of k vertices unmatched. The matching M ′ S ∪ M ′′ is then perfect.  ... 
doi:10.4171/owr/2006/48 fatcat:cnquryyfpba6bhuesmwsx2vq34

Derandomization through approximation

David R. Karger, Rajeev Motwani
1994 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing - STOC '94  
We show that the minimum cut and multi-cut problems in weighted undirected graphs can be solved in JVC. We do so by giving three separate and independently interesting results.  ...  The first is an m2/n proces-Permission to co y without fee all or part of this material is J' granted provide that the copies are not made or distributed for direct commercial advantage, the ACM copyright  ...  They show that for sufficiently large n, there exists a graph Gn on n vertices with the following properties: the graph is 7-regular; it has a constant expansion factor; and, for some constant c, the second  ... 
doi:10.1145/195058.195241 fatcat:k2et7dvjsrfoldxxsrihokmrwi

Perfect hashing

Zbigniew J. Czech, George Havas, Bohdan S. Majewski
1997 Theoretical Computer Science  
C is O(nlog n).  ...  As the mapping step runs in O(n) expected time, and the optimized ordering step needs O(n) time, FHCD made a claim that their minimal perfect hash function algorithm runs practically in O(n) time, however  ...  The rest of the symbols we use may have different meanings depending on the chapter in which the symbols occur.  ... 
doi:10.1016/s0304-3975(96)00146-6 fatcat:htaph24frffzjevl2q6kxz467e
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