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Weighted Matchings via Unweighted Augmentations [article]

Buddhima Gamlath, Sagar Kale, Slobodan Mitrović, Ola Svensson
2018 arXiv   pre-print
We design a generic method for reducing the task of finding 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.  ... 
arXiv:1811.02760v1 fatcat:7rw6klxh6rfzdoxe24cpaothoq

Maximum-weight bipartite matching technique and its application in image feature matching

Yong-Qing Cheng, Victor Wu, Robert Collins, Allen R. Hanson, Edward M. Riseman, Rashid Ansari, Mark J. T. Smith
1996 Visual Communications and Image Processing '96  
It is shown that the image feature 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 .  ... 
doi:10.1117/12.233261 fatcat:n4klhxix7zdchmsigvnkn3miza

Almost Optimal Stochastic Weighted Matching With Few Queries [article]

Soheil Behnezhad, Nima Reyhani
2018 arXiv   pre-print
To obtain our results, we introduce novel properties of a generalization of 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.  ... 
arXiv:1710.10592v3 fatcat:zqcozarlvjd4ph2pdfmwe6qybu

Decomposition theorems for square-free2-matchings in bipartite graphs

Kenjiro Takazawa
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  ... 
doi:10.1016/j.dam.2017.07.035 fatcat:4kq5ksd665bpxje5ijmhx65y4q

Improved Bounds for Distributed Load Balancing [article]

Sepehr Assadi, Aaron Bernstein, Zachary Langley
2020 arXiv   pre-print
[SPAA 2015] showed an O(logn/loglogn)-approximation for 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  ... 
arXiv:2008.04148v2 fatcat:mk7rzay5srf3dofkkvs7fpr2si

Improved Bounds for Distributed Load Balancing

Sepehr Assadi, Aaron Bernstein, Zachary Langley, Hagit Attiya
2020 International Symposium on Distributed Computing  
[SPAA 2015] showed an O(log n / log log n)-approximation for 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.  ... 
doi:10.4230/lipics.disc.2020.1 dblp:conf/wdag/AssadiBL20 fatcat:2ftzwvm5sjgfneexkahuelfxva

Discriminative importance weighting of augmented training data for acoustic model training

Sunit Sivasankaran, Emmanuel Vincent, Irina Illina
2017 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
Data 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.  ... 
doi:10.1109/icassp.2017.7953085 dblp:conf/icassp/SivasankaranVI17 fatcat:dw4jznujjjhghefz67n7hinrz4

Distributed Approximation of Maximum Independent Set and Maximum Matching [article]

Reuven Bar-Yehuda, Keren Censor-Hillel, Mohsen Ghaffari, Gregory Schwartzman
2017 arXiv   pre-print
Next, we show that for maximum 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.  ... 
arXiv:1708.00276v1 fatcat:dpukt4uggfhtdnecarnqjk2iym

A Fast Approximation for Maximum Weight Matroid Intersection

Chandra Chekuri, Kent Quanrud
2015 Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms  
An exact algorithm for finding a maximum cardinality independent set (the 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.  ... 
doi:10.1137/1.9781611974331.ch33 dblp:conf/soda/ChekuriQ16 fatcat:nhtoq7xybfhmfcromq7ie4cmsu

Distributed Maximum Matching in Bounded Degree Graphs [article]

Guy Even, Moti Medina, Dana Ron
2014 arXiv   pre-print
We present deterministic distributed algorithms for computing approximate maximum cardinality 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, [  ... 
arXiv:1407.7882v3 fatcat:pliy7e2xerhnzntfdfmemwsrfu

Stabilizing Weighted Graphs [article]

Zhuan Khye Koh, Laura Sanità
2017 arXiv   pre-print
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.  ...  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.  ... 
arXiv:1709.01982v2 fatcat:z6j62mronrdzjdk7el74raiike

Standing Data Disproves Biomechanical Mechanism for Balance-Based Torso-Weighting

Ajay Crittendon, Danielle O'Neill, Gail L. Widener, Diane D. Allen
2014 Archives of Physical Medicine and Rehabilitation  
Conclusions-If BBTW worked 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  ... 
doi:10.1016/j.apmr.2013.08.235 pmid:24001445 pmcid:PMC3918424 fatcat:yq3qcbai3zfprec2x33wrikfui

Fast Scheduling of Weighted Unit Jobs with Release Times and Deadlines [chapter]

C. Greg Plaxton
2008 Lecture Notes in Computer Science  
This job scheduling problem can also be viewed as a special case of 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.  ... 
doi:10.1007/978-3-540-70575-8_19 fatcat:p23a5kb2bbainhyq6jzpb6tmjm

Stabilizing Weighted Graphs

Zhuan Khye Koh, Laura Sanità, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
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.  ...  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.  ... 
doi:10.4230/lipics.icalp.2018.83 dblp:conf/icalp/KohS18 fatcat:yg2xxp5uorbajlj2grkt3doijq

Exact and Approximation Algorithms for Weighted Matroid Intersection

Chien-Chung Huang, Naonori Kakimura, Naoyuki Kamiyama
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 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] .  ... 
doi:10.1137/1.9781611974331.ch32 dblp:conf/soda/HuangKK16 fatcat:5equnj4pjnenlbgr4oddz2gps4
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