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Engineering Fast Almost Optimal Algorithms for Bipartite Graph Matching

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. ...

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

2021
*
arXiv
*
pre-print

This problem is a restricted version of minimum-weight edge cover

arXiv:2109.07524v1
fatcat:lsn7krpny5h2ficsofbbxexczy
*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. ...##
###
A Quest for Structure in Complexity

2017
*
Bulletin of the European Association for Theoretical Computer Science
*

The class SPL contains

dblp:journals/eatcs/ArvindM17
fatcat:axk2knwgpbh6nfdz3bespdpqom
*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. ...##
###
Tight Bounds for Testing Bipartiteness in General Graphs

2004
*
SIAM journal on computing (Print)
*

We present an algorithm whose complexity isÕ(min( √

doi:10.1137/s0097539703436424
fatcat:rrqzskk4sfeajc4dela2zewjpy
*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). ...##
###
On approximating the d -girth of a graph

2013
*
Discrete Applied Mathematics
*

algorithms

doi:10.1016/j.dam.2013.04.022
fatcat:5zzhqyjmzjglpeufl2t2fixxtu
*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 . ...##
###
On Approximating the d-Girth of a Graph
[chapter]

2011
*
Lecture Notes in Computer Science
*

algorithms

doi:10.1007/978-3-642-18381-2_39
fatcat:24lhgvf2ijakbmzxegjzg7utcy
*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 . ...##
###
Bounds on the maximum multiplicity of some common geometric graphs
[article]

2011
*
arXiv
*
pre-print

We give a combinatorial characterization of the longest tours, which leads to an

arXiv:1012.5664v2
fatcat:2mjbkstpr5e7ndjdlmlttk6iwa
*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 . ...##
###
On the ?log rank?-conjecture in communication complexity

1995
*
Combinatorica
*

We consider the following problem: each of two players gets a

doi:10.1007/bf01192528
fatcat:gay75pongrfdrox2do2ectkrtq
*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. ...##
###
View-based object recognition using saliency maps

1999
*
Image and Vision Computing
*

To compare two saliency map

doi:10.1016/s0262-8856(98)00124-3
fatcat:e2thtjp2fbf6hdbpfeuagep2wq
*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] . ...##
###
Near-Optimal Induced Universal Graphs for Bounded Degree Graphs
[article]

2016
*
arXiv
*
pre-print

For the family of all undirected

arXiv:1607.04911v2
fatcat:o4pfu5umi5hzpcjm2xu7bswla4
*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. ...##
###
Generation of synthetic sequential benchmark circuits

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

doi:10.1145/258305.258333
dblp:conf/fpga/HuttonRC97
fatcat:mog6d4lhbfb4dhfm2yb4m5lyka
*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. ...##
###
Counting truth assignments of formulas of bounded tree-width or clique-width

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) . ...

##
###
Combinatorics, Probability and Computing

2006
*
Oberwolfach Reports
*

The meeting was dedicated to recent developments

doi:10.4171/owr/2006/48
fatcat:cnquryyfpba6bhuesmwsx2vq34
*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*. ...##
###
Derandomization through approximation

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

doi:10.1145/195058.195241
fatcat:k2et7dvjsrfoldxxsrihokmrwi
*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 ...##
###
Perfect hashing

1997
*
Theoretical Computer Science
*

C is

doi:10.1016/s0304-3975(96)00146-6
fatcat:htaph24frffzjevl2q6kxz467e
*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. ...
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