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Maximum Induced Matching Algorithms via Vertex Ordering Characterizations
[article]

2017
*
arXiv
*
pre-print

Furthermore, these

arXiv:1707.01245v2
fatcat:4jfjrdyjn5dfpcpqsl2hlu2gfu
*orderings*on L2(g) can be exploited*algorithmically*to compute a*maximum**induced**matching*on G faster. ... We study the*maximum**induced**matching*problem on a graph g.*Induced**matchings*correspond to independent sets in L2(g), the square of the line graph of g. ...*Algorithm*2 2 Cocomparability Weighted*Maximum**Induced**Matching*(CCWMIM) Input: G = (V, E, w) an edge weighted cocomparability graph where w : E ae R >0 Output: A*maximum*weight*induced**matching*of G 1 ...##
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Maximum Induced Matching Algorithms via Vertex Ordering Characterizations * †

unpublished

Furthermore, these

fatcat:ykjsc77of5fitlqmi7n2xknfxu
*orderings*on L 2 (G) can be exploited*algorithmically*to compute a*maximum**induced**matching*on G faster. ... We study the*maximum**induced**matching*problem on a graph G.*Induced**matchings*correspond to independent sets in L 2 (G), the square of the line graph of G. ... In Section 4, we present the*maximum*weight*induced**matching**algorithm*and its analysis on cocomparability graphs. ...##
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Vertex-Weighted Matching in Two-Directional Orthogonal Ray Graphs
[chapter]

2013
*
Lecture Notes in Computer Science
*

Given such a compact representation of G, and a (possibly negative) weight for each

doi:10.1007/978-3-642-45030-3_49
fatcat:ekrg335yazhmnj3ybw6rtuv5su
*vertex*, we show how to compute a*maximum*weight*matching*of G in O(n log 2 n) time. ... As an application of our more general result, we obtain an O(n log 2 n)-time*algorithm*for computing the VCG outcome of a sealed-bid unit-demand auction in which each item has two associated numerical ... Assume that we are given a bicolored 2D-graph representation of an n-*vertex*,*vertex*-weighted 2DORG G such that each x-value, y-value, or weight is an O(1)-word integer. ...##
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Mapping Matchings to Minimum Vertex Covers: Kőnig's Theorem Revisited
[article]

2020
*
arXiv
*
pre-print

Kőnig's proof of this fact gave an

arXiv:2004.08636v1
fatcat:hegddchyivc4bfjdjvqgx5myw4
*algorithm*for finding a minimum*vertex*cover from a*maximum**matching*. ... We find that all minimum*vertex*covers can be found by applying this*algorithm*to some*matching*and then classify which*matchings*give minimum*vertex*covers when this*algorithm*is applied to them. ... This*algorithm*is still used in most state of the art*algorithms*today in*order*to find a minimum*vertex*cover after finding a*maximum**matching*(which may be accomplished by one of several different*algorithms*...##
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The Sparse Awakens: Streaming Algorithms for Matching Size Estimation in Sparse Graphs

2017
*
European Symposium on Algorithms
*

In contrast to prior work, our results take more advantage of the streaming access to the input and

doi:10.4230/lipics.esa.2017.29
dblp:conf/esa/CormodeJMM17
fatcat:ehrv3bs7zvf6rmeli6s6p46x3y
*characterize*the*matching*size based on the*ordering*of the edges in the stream in addition to the degree ... We present improved streaming*algorithms*for approximating the size of*maximum**matching*with sparse (bounded arboricity) graphs. ... We prove this*characterization*gives an O(α) approximation of the*maximum**matching*size. ...##
###
The Sparse Awakens: Streaming Algorithms for Matching Size Estimation in Sparse Graphs
[article]

2016
*
arXiv
*
pre-print

In contrast to the previous works, our results take more advantage of the streaming access to the input and

arXiv:1608.03118v2
fatcat:qds4khoq3beohpdsxs2mduibqq
*characterize*the*matching*size based on the*ordering*of the edges in the stream in addition to ... arboricity graph, we present a one-pass*algorithm*that uses space O (c^10/3n^2/3) and returns an O(c)-estimator for the size of the*maximum**matching*. ... In the following we let M µ denote the size of*maximum**matching*in G L . Let G L = (V ′ , E ′ ) be an*induced*subgraph of G where V ′ = {v| deg G (v) ≤ µ}*Characterization*lemmas Lemma 3 ([9] ). ...##
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Optimal Lower Bounds for Matching and Vertex Cover in Dynamic Graph Streams
[article]

2020
*
arXiv
*
pre-print

[SODA 2016] gave an optimal space lower bound for insertion-deletion streaming

arXiv:2005.11116v1
fatcat:ftmesaopxregvokon4gwq56b4i
*algorithms*for*Maximum**Matching**via*the simultaneous model of communication. ... Our results imply optimal space lower bounds for insertion-deletion streaming*algorithms*for*Maximum**Matching*and Minimum*Vertex*Cover. Previously, Assadi et al. ...*induced**matchings*. ...##
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Optimal Lower Bounds for Matching and Vertex Cover in Dynamic Graph Streams

2020
*
Computational Complexity Conference
*

[SODA 2016] gave an optimal space lower bound for insertion-deletion streaming

doi:10.4230/lipics.ccc.2020.30
dblp:conf/coco/DarkK20
fatcat:wdnnzaful5avfb7pexxkts3gqq
*algorithms*for*Maximum**Matching**via*the simultaneous model of communication. ... Our results imply optimal space lower bounds for insertion-deletion streaming*algorithms*for*Maximum**Matching*and Minimum*Vertex*Cover. Previously, Assadi et al. ...*induced**matchings*. ...##
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On the strong p-Helly property

2008
*
Discrete Applied Mathematics
*

We describe a

doi:10.1016/j.dam.2007.05.047
fatcat:ly2qavmkpjclfhb6jki5hi3zda
*characterization*for this class and obtain an*algorithm*for recognizing such graphs. ... In this paper, we*characterize*strong p-Helly hypergraphs. This*characterization*leads to an*algorithm*for recognizing such hypergraphs, which terminates within polynomial time whenever p is fixed. ... This means that V int ⊆ U and the vertices of V int and V ext form an*induced*k + -*matching*in G. The rank of H is the*maximum*size of a hyperdge of H. ...##
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A Network Game with Attackers and a Defender

2007
*
Algorithmica
*

So, using a polynomial time

doi:10.1007/s00453-007-9109-3
fatcat:ttarahtkgfeejiyqr527muums4
*algorithm*to compute a*Maximum**Matching*for a bipartite graph, we obtain, as our main result, a deterministic, polynomial time*algorithm*to compute a*Matching*Nash equilibrium ... The*characterization*enables a non-deterministic, polynomial time*algorithm*to compute a*Matching*Nash equilibrium for any such graph. -Bipartite graphs are shown to satisfy the*characterization*. ... a Minimum*Vertex*Cover V C of a bipartite graph (*via*reduction to computing a*Maximum**Matching*), followed by setting IS to include all vertices in the complementary*vertex*set of V C. ...##
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The Price of Defense
[chapter]

2006
*
Lecture Notes in Computer Science
*

In particular, we prove that in a

doi:10.1007/11821069_62
fatcat:jejk3ielevav3manzez6ijhpn4
*Matching*Nash equilibrium, the support of the*vertex*players is a*Maximum*Independent Set of the graph (Proposition 5.1) and the support of the edge player is a Minimum ... Each attacker (called a*vertex*player) targets a node of the network chosen*via*its own probability distribution on nodes; the defender (called the edge player) chooses a single link*via*its own probability ... In turn, the graph-theoretic*algorithm*relies on computing a Minimum Edge Cover (*via*computing a*Maximum**Matching*) and a subsequent reduction to 2SAT. • We prove that the Price of Defense for a*Matching*...##
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Stabilizing Weighted Graphs

2018
*
International Colloquium on Automata, Languages and Programming
*

Motivated by this, in the last few years many researchers have investigated the

doi:10.4230/lipics.icalp.2018.83
dblp:conf/icalp/KohS18
fatcat:yg2xxp5uorbajlj2grkt3doijq
*algorithmic*problem of turning a given graph into a stable one,*via*edge-and*vertex*-removal operations. ... An edge-weighted graph G = (V, E) is called stable if the value of a*maximum*-weight*matching*equals the value of a*maximum*-weight fractional*matching*. ... Our first step is to*characterize*basic*maximum*-weight fractional*matchings*which have more than γ(G) odd cycles. ...##
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A parallel algorithm for computing the critical independence number and related sets

2012
*
Ars Mathematica Contemporanea
*

The graph

doi:10.26493/1855-3974.165.b8b
fatcat:tzvoqqkbcnckzlaogb2wwqwhfu
*induced*on this set is a König-Egerváry graph whose components are either isolated vertices or which have perfect*matchings*. ... It is demonstrated here that there is a parallel*algorithm*using n processors that runs in O(n 1.5 m/ log n) time. The new*algorithm*returns the union of all*maximum*critical independent sets. ... If M is a*matching*in a graph G and w is a*vertex*incident to an edge in M , let w be the*vertex**matched*to w under M . The new*algorithm*can now be stated. The parallelism occurs in step 1. ...##
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Computing cutwidth and pathwidth of semi-complete digraphs via degree orderings
[article]

2012
*
arXiv
*
pre-print

In this work we introduce a new approach to computing these width measures on semi-complete digraphs,

arXiv:1210.5363v1
fatcat:etv4uiqbtfdhzhdv3cgefh7b5y
*via*degree*orderings*. ... First, we present polynomial-time approximation*algorithms*for both cutwidth and pathwidth, faster and simpler than the previously known ones; the most significant improvement is in case of pathwidth, ... Moreover, we have that every*vertex*of N (A) must be in fact*matched*to a*vertex*of A, as the vertices*matched*to N (A) are also reachable*via*alternating paths from A 0 . ...##
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An exact characterization of tractable demand patterns for maximum disjoint path problems
[article]

2014
*
arXiv
*
pre-print

of large

arXiv:1411.0871v1
fatcat:axr6lrw2jjfcphrdrs7tkvbw7i
*induced**matchings*and large*induced*skew bicliques in the demand graph H (a skew biclique is a bipartite graph on vertices a_1, ..., a_n, b_1, ..., b_n with a_i and b_j being adjacent if and ... If H does not contain every*matching*and does not contain every skew biclique, then H-*Maximum*Disjoint Paths is FPT. 2. ... Excluding*induced**matchings*and skew bicliques: the exact FPT*algorithm*The goal of this section is to prove the*algorithmic*part of Theorem 1.4: an FPT*algorithm*for*Maximum*Disjoint H-Paths if H does ...
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