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Weighted Matchings via Unweighted Augmentations
[article]

2018
*
arXiv
*
pre-print

We design a generic method for reducing the task of finding

arXiv:1811.02760v1
fatcat:7rw6klxh6rfzdoxe24cpaothoq
*weighted**matchings*to that of finding short*augmenting*paths in*unweighted*graphs. ... -approximate maximum*weighted**matching*. ... As we elaborate below, the result is achieved*via*a general approach that reduces the task of finding*weighted**matchings*to that of finding (short)*unweighted**augmenting*paths. ...##
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Maximum-weight bipartite matching technique and its application in image feature matching

1996
*
Visual Communications and Image Processing '96
*

It is shown that the image feature

doi:10.1117/12.233261
fatcat:n4klhxix7zdchmsigvnkn3miza
*matching*problem can be reduced to an*unweighted**matching*problem in the bipartite graphs. ... It is further shown that the problem can be formulated as the general maximum-*weight*bipartite*matching*problem, thus generalizing the above u n*weighted*bipartite*matching*technique. ... Indeed, it was proved that if we repeatedly perform*augmentations*using*augmenting*paths of maximum incremental*weight*, this process yields a maximum-*weight**matching*M 14 w . ...##
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Almost Optimal Stochastic Weighted Matching With Few Queries
[article]

2018
*
arXiv
*
pre-print

To obtain our results, we introduce novel properties of a generalization of

arXiv:1710.10592v3
fatcat:zqcozarlvjd4ph2pdfmwe6qybu
*augmenting*paths to*weighted**matchings*that may be of independent interest. ... We consider the stochastic*matching*problem. ... Roughly speaking, these claims are correct since in*unweighted*graphs, each*augmenting*path increases the size of a*matching*by at most one edge. ...##
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Decomposition theorems for square-free2-matchings in bipartite graphs

2017
*
Discrete Applied Mathematics
*

*Weighted*k ≥ n/2 NP-hard NP-hard k ≥ 5 k = 4 k = 3 k = 2 P P Complexity NP-hard (Papadimitriou '78) P (Hartvigsen '84) OPEN NP-hard NP-hard (Vornberger '80) OPEN Bipartite

*Unweighted*

*Weighted*k ≥ n/2 ... , van der Ster, Stougie '11 • Correa, Larré, Soto '12 • Karp, Ravi '14 • T. '15 Connectivity

*augmentation*Kobayashi '12 Relaxation of the Hamilton cycle problem Relax Application to Approximation 6 ...

*Unweighted*

*Weighted*k ≥ n/2 NP-hard NP-hard k ≥ 6 k = 4 k = 2 P P NP-hard (Geelen '99) NP-hard (Geelen '99) P (Hartvigsen '06, Pap '07) NP-hard (Király '03) Edge-

*weight*is vertex-induced ...

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Improved Bounds for Distributed Load Balancing
[article]

2020
*
arXiv
*
pre-print

[SPAA 2015] showed an O(logn/loglogn)-approximation for

arXiv:2008.04148v2
fatcat:mk7rzay5srf3dofkkvs7fpr2si
*unweighted*clients and O(log^2n/loglogn)-approximation for*weighted*clients with round-complexity polylog(n). ... In the CONGEST model, we give an O(1)-approximation algorithm in polylog(n) rounds for*unweighted*clients. For*weighted*clients, the approximation ratio is O(logn). ... load balancing [4, 11] : if a graph contains some client-perfect (κ, τ )-*matching*, then every (κ, 2τ )-*matching*is either client-perfect or can be*augmented**via*an*augmenting*path of logarithmic length ...##
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Improved Bounds for Distributed Load Balancing

2020
*
International Symposium on Distributed Computing
*

[SPAA 2015] showed an O(log n / log log n)-approximation for

doi:10.4230/lipics.disc.2020.1
dblp:conf/wdag/AssadiBL20
fatcat:2ftzwvm5sjgfneexkahuelfxva
*unweighted*clients and O(log²n/log log n)-approximation for*weighted*clients with round-complexity polylog(n). ... This problem has a variety of applications and has been widely studied under several different names, including: scheduling with restricted assignment, semi-*matching*, and distributed backup placement. ... Our analysis, by contrast, directly exploits the non-existence of short*augmenting*paths*via*Lemma 3. ...##
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Discriminative importance weighting of augmented training data for acoustic model training

2017
*
2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
*

Data

doi:10.1109/icassp.2017.7953085
dblp:conf/icassp/SivasankaranVI17
fatcat:dw4jznujjjhghefz67n7hinrz4
*augmentation*was done by adding noise at different SNRs. A relative WER improvement of 15% was obtained with the proposed data*weighting*algorithm compared to the*unweighted**augmented*dataset. ... In this work we propose an algorithm to automatically*weight*data perturbed using a variety of*augmentation*techniques and/or parameters. ... In the first step, given the data*weights*ω, the DNN parameters θ are updated*via*one epoch of SGD on the full training set. ...##
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Distributed Approximation of Maximum Independent Set and Maximum Matching
[article]

2017
*
arXiv
*
pre-print

Next, we show that for maximum

arXiv:1708.00276v1
fatcat:dpukt4uggfhtdnecarnqjk2iym
*weight**matching*, relaxing the approximation factor to (2+ε) allows us to devise a distributed algorithm requiring O(Δ/Δ) rounds for any constant ε>0. ... We then show how to use our MaxIS approximation algorithms to compute a 2-approximation for maximum*weight**matching*without incurring any additional round penalty in the CONGEST model. ...*unweighted**matching*. ...##
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A Fast Approximation for Maximum Weight Matroid Intersection

2015
*
Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms
*

An exact algorithm for finding a maximum cardinality independent set (the

doi:10.1137/1.9781611974331.ch33
dblp:conf/soda/ChekuriQ16
fatcat:nhtoq7xybfhmfcromq7ie4cmsu
*unweighted*case), due to Cunningham, runs in O(nk 1.5 Q) time. ... There are also scaling based algorithms that run in O(n 2 √ k log(kW )Q) time, where W is the maximum*weight*(assuming all*weights*are integers), and ellipsoid-style algorithms that run in O n 2 log(n) ... Scaling is a powerful methodology for solving*weighted*problems*via*algorithms for the corresponding*unweighted*problem. ...##
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Distributed Maximum Matching in Bounded Degree Graphs
[article]

2014
*
arXiv
*
pre-print

We present deterministic distributed algorithms for computing approximate maximum cardinality

arXiv:1407.7882v3
fatcat:pliy7e2xerhnzntfdfmemwsrfu
*matchings*and approximate maximum*weight**matchings*. ... Our algorithm for the edge-*weighted*case computes a*matching*whose*weight*is at least (1-) times the optimal in ({1/,n/})^O(1/)·(Δ^O(1/)+^*(n)) rounds for edge-*weights*in [,1]. ... The main difference between the algorithms for the*weighted*case and the*unweighted*case is that the maximum length of the*augmenting*paths (and cycles) does not grow; instead, during every step, (M, [ ...##
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Stabilizing Weighted Graphs
[article]

2017
*
arXiv
*
pre-print

An edge-

arXiv:1709.01982v2
fatcat:z6j62mronrdzjdk7el74raiike
*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*. ... However, all the algorithmic results developed in the literature so far only hold for*unweighted*instances, i.e., assuming unit*weights*on the edges of G. ...*matchings*in*unweighted*graphs. ...##
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Standing Data Disproves Biomechanical Mechanism for Balance-Based Torso-Weighting

2014
*
Archives of Physical Medicine and Rehabilitation
*

Conclusions-If BBTW worked

doi:10.1016/j.apmr.2013.08.235
pmid:24001445
pmcid:PMC3918424
fatcat:yq3qcbai3zfprec2x33wrikfui
*via*a biomechanical shift of the center of mass, COP changes should*match*the direction of greatest*weighting*with BBTW. Our data allowed us to reject this ... Direction of greatest*weight*placement did not*match*the direction of change in average COP in the majority of participants with multiple sclerosis or the healthy controls in EO or EC conditions (p<.0001 ... The authors thank Cynthia Gibson-Horn, PT, who performed the BBTW assessment and*weighting*protocol for all participants in this study.*Weight*Placement for Two Participants and Whether ...##
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Fast Scheduling of Weighted Unit Jobs with Release Times and Deadlines
[chapter]

2008
*
Lecture Notes in Computer Science
*

This job scheduling problem can also be viewed as a special case of

doi:10.1007/978-3-540-70575-8_19
fatcat:p23a5kb2bbainhyq6jzpb6tmjm
*weighted*bipartite*matching*: each job represents a vertex on the left side of the bipartite graph; each time slot represents a vertex ...*weight*. ... The*unweighted*version of the above scheduling problem is equivalent to a special case of bipartite*matching*called "convex" bipartite*matching*. ...##
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Stabilizing Weighted Graphs

2018
*
International Colloquium on Automata, Languages and Programming
*

An edge-

doi:10.4230/lipics.icalp.2018.83
dblp:conf/icalp/KohS18
fatcat:yg2xxp5uorbajlj2grkt3doijq
*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*. ... However, all the algorithmic results developed in the literature so far only hold for*unweighted*instances, i.e., assuming unit*weights*on the edges of G. ...*matchings*in*unweighted*graphs. ...##
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Exact and Approximation Algorithms for Weighted Matroid Intersection

2015
*
Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms
*

To be precise, we show that we can find an exact solution

doi:10.1137/1.9781611974331.ch32
dblp:conf/soda/HuangKK16
fatcat:5equnj4pjnenlbgr4oddz2gps4
*via*solving W*unweighted*matroid intersections problems, where W is the largest given*weight*. ... Furthermore, we can find a (1 − ϵ)-approximate solution*via*solving O(ϵ −1 log r)*unweighted*matroid intersection problems, where r is the smallest rank of the given two matroids. ... Examples include maximum*weight**matching*[8] , shortest paths [41] , and maximum flow [4, 27, 32] . ...
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