Filters








1,184 Hits in 5.5 sec

Semi-matchings for bipartite graphs and load balancing

Nicholas J.A. Harvey, Richard E. Ladner, László Lovász, Tami Tamir
2006 Journal of Algorithms  
We present a way to evaluate the quality of a given semi-matching and show that, under this measure, an optimal semimatching balances the load on the right hand vertices with respect to any Lp-norm.  ...  We consider the problem of fairly matching the left-hand vertices of a bipartite graph to the right-hand vertices.  ...  The primary contributions of this paper are: (1) the semi-matching model for solving load balancing problems of the form described above, (2) two efficient algorithms for computing optimal semi-matchings  ... 
doi:10.1016/j.jalgor.2005.01.003 fatcat:hyww3ixtkfcjdjj23yl5as5ljm

Semi-matchings for Bipartite Graphs and Load Balancing [chapter]

Nicholas J. A. Harvey, Richard E. Ladner, László Lovász, Tami Tamir
2003 Lecture Notes in Computer Science  
We present a way to evaluate the quality of a given semi-matching and show that, under this measure, an optimal semimatching balances the load on the right hand vertices with respect to any Lp-norm.  ...  We consider the problem of fairly matching the left-hand vertices of a bipartite graph to the right-hand vertices.  ...  The primary contributions of this paper are: (1) the semi-matching model for solving load balancing problems of the form described above, (2) two efficient algorithms for computing optimal semi-matchings  ... 
doi:10.1007/978-3-540-45078-8_26 fatcat:isixicnpzbebxp6ulq5uei7gza

On Load-Balanced Semi-matchings for Weighted Bipartite Graphs [chapter]

Chor Ping Low
2006 Lecture Notes in Computer Science  
In this paper, we prove that the problem of finding a semi-matching that minimizes the maximum load among all vertices in a weighted bipartite graph is NP-complete.  ...  A semi-matching on a bipartite graph G = (U ∪V, E) is a set of edges X ⊆ E such that each vertex in U is incident to exactly one edge in X.  ...  Harvey et. al.[3] consider the problem of finding semi-matchings for unweighted bipartite graphs with the objective of balancing the load 1 of the vertices in V under any L p -norm.  ... 
doi:10.1007/11750321_15 fatcat:tl33jigkhngtffeqgro5b7cwf4

Optimal Balanced Semi-Matchings for Weighted Bipartite Graphs

Yuta Harada, Hirotaka Ono, Kunihiko Sadakane, Masafumi Yamashita
2007 IPSJ Digital Courier  
In this paper, We formulate the min-weight load-balancing problem of finding a balanced semi-matching that minimizes the total weight for weighted bipartite graphs.  ...  The semi-matching is an extension of the matching for a bipartite graph G = (U ∪ V, E). It is defined as a set of edges, M ⊆ E, such that each vertex in U is an endpoint of exactly one edge in M .  ...  Acknowledgments This work is supported in part by the Grant-in-Aid of the Ministry of Education, Science, Sports and Culture of Japan.  ... 
doi:10.2197/ipsjdc.3.693 fatcat:gmfsggqwgfeb3khlkwwesjdfje

The Symbolic OBDD Algorithm for Finding Optimal Semi-matching in Bipartite Graphs

Tianlong Gu, Liang Chang, Zhoubo Xu
2011 Communications and Network  
The optimal semi-matching problem is one relaxing form of the maximum cardinality matching problems in bipartite graphs, and finds its applications in load balancing.  ...  We present novel symbolic OBDD formulation and algorithm for the optimal semimatching problem in bipartite graphs.  ...  Motivated by load balancing problem, Harvey et al. defined the optimal semi-matching problem through relaxing maximum cardinality matching in bipartite graphs [3] .  ... 
doi:10.4236/cn.2011.32009 fatcat:epvy7rhenrgozogy7k54ueu54m

Approximation Algorithm for Scheduling Parallel Machines with Machine Eligibility Restrictions and special jobs

2016 Journal of Engineering Mechanics and Machinery  
And the processing times of jobs are restricted to one of two values, 1 andε. A semi-matching model G= [J∪M,E,W] is presented to formulate this scheduling problem.  ...  The main idea of the improvement algorithm is to construct alternating tree, then to find the optimal alternating path for each vertex in M iteratively.  ...  Acknowledgements This work is financially supported by the Research Fund for the Doctoral Program of Higher Education, China(20132304120021); and by the National Natural Science Foundation of China (51275104  ... 
doi:10.23977/jemm.2016.11005 fatcat:losf4w3iwvac7p4fvj6t2nn2pi

Locally Optimal Load Balancing [chapter]

Laurent Feuilloley, Juho Hirvonen, Jukka Suomela
2015 Lecture Notes in Computer Science  
This work studies distributed algorithms for locally optimal load-balancing: We are given a graph of maximum degree ∆, and each node has up to L units of load.  ...  For the general case (∆ > 2), we show that fractional load balancing can be solved in poly(L, ∆) rounds and discrete load balancing in f (L, ∆) rounds for some function f , independently of the number  ...  Mitchell, Pekka Orponen, Joel Rybicki, Thomas Sauerwald, Stefan Schmid, and Jara Uitto. Many thanks to all of you for your comments!  ... 
doi:10.1007/978-3-662-48653-5_36 fatcat:x7e47hecpjf7pjoc4uude3x6qa

Locally Optimal Load Balancing [article]

Laurent Feuilloley, Juho Hirvonen, Jukka Suomela
2015 arXiv   pre-print
This work studies distributed algorithms for locally optimal load-balancing: We are given a graph of maximum degree Δ, and each node has up to L units of load.  ...  For the general case (Δ > 2), we show that fractional load balancing can be solved in poly(L,Δ) rounds and discrete load balancing in f(L,Δ) rounds for some function f, independently of the number of nodes  ...  Mitchell, Pekka Orponen, Joel Rybicki, Thomas Sauerwald, Stefan Schmid, and Jara Uitto. Many thanks to all of you for your comments!  ... 
arXiv:1502.04511v1 fatcat:omoancs5qfhv3mfsyr6zwhfkoa

Exploiting locality in distributed SDN control

Stefan Schmid, Jukka Suomela
2013 Proceedings of the second ACM SIGCOMM workshop on Hot topics in software defined networking - HotSDN '13  
provider footprint ...  Optimization: Latency and load-balancing  Latency e.g., FIBIUM  Handling certain events close to datapath and shield/load-balance more global controllers (e.g., Kandoo) Alice  ...  Vision:  Control becomes distributed  Controllers become near-sighted (control part of network or flow space) Why:  Enables wide-area SDN networks  Administrative: Alice and Bob  Admin. domains, local  ...  SDN for TE and Load-Balancing: Re-Route Flows Compute and Ensure Loop-Free Forwarding Set SDN Task 1: Link Assignment ("Semi-Matching Problem") 5 Stefan Schmid (T-Labs) fully central fully local  ... 
doi:10.1145/2491185.2491198 dblp:conf/sigcomm/SchmidS13 fatcat:wzulolvmgvcfdcqdo3co2zokky

Maximum semi-matching problem in bipartite graphs

Ján Katrenič, Gabriel Semanišin
2013 Discussiones Mathematicae Graph Theory  
An (f,g)-semi-matching in a bipartite graph G=(U ∪ V,E) is a set of edges M ⊆ E such that each vertex u∈ U is incident with at most f(u) edges of M, and each vertex v∈ V is incident with at most g(v) edges  ...  In this paper we give an algorithm that for a graph with n vertices and m edges, n< m, constructs a maximum (f,g)-semi-matching in running time O(m· (√(∑_u∈ Uf(u)), √(∑_v∈ Vg(v)))).  ...  Acknowledgement The research of both authors was partially supported by Slovak APVV grants APVV-0035-10 and SK-SI-0014-10.  ... 
doi:10.7151/dmgt.1694 fatcat:jtsz7gx2pvcvfajmevtdussstq

Online Bipartite Matching with Amortized O(^2 n) Replacements [article]

Aaron Bernstein, Jacob Holm, Eva Rotenberg
2018 arXiv   pre-print
In the online bipartite matching problem with replacements, all the vertices on one side of the bipartition are given, and the vertices on the other side arrive one by one with all their incident edges  ...  We show that if the final graph has maximum server load L, then the SAP protocol makes amortized O( {L ^2 n , √(n) n}) reassignments.  ...  The authors would like to thank Seffi Naor for pointing out to us that uniqueness of server loads can be proved via convex optimization (Section 3.2.1), and to thank Martin Skutella and Guilamme Sagnol  ... 
arXiv:1707.06063v4 fatcat:vge4e6tkvrdfvprzgz7uwkdnby

Online Bipartite Matching with Amortized O(log 2 n) Replacements

Aaron Bernstein, Jacob Holm, Eva Rotenberg
2019 Journal of the ACM  
They also show that if the bipartite graph remains a forest, there exists an algorithm (not SAP) with O(n log n) replacements, and a matching lower bound.  ...  The problem of online bipartite matchings with replacements was introduced in 1995 by Grove, Kao, Krishnan, and Vitter [13], who showed matching upper and lower bounds of Θ(n log n) replacements for the  ...  flow [9, 10] , and in Hopcroft and Karp's algorithm for maximum matching in bipartite graphs [19] .  ... 
doi:10.1145/3344999 fatcat:2krkte564jh4bheagk23jdvhx4

Semi-Matching Algorithms for Scheduling Parallel Tasks under Resource Constraints

Anne Benoit, Johannes Langguth, Bora Ucar
2013 2013 IEEE International Symposium on Parallel & Distributed Processing, Workshops and Phd Forum  
This problem is related to the minimum makespan scheduling problem on unrelated machines, as well as to the concurrent job shop problem, and it amounts to finding a semi-matching in bipartite graphs or  ...  The problem is known to be NP-complete for bipartite graphs with general vertex (task) weights, and solvable in polynomial time for unweighted graphs (i.e., unit-weight tasks).  ...  In this case, the hypergraph is in fact a bipartite graph, and the problem consists therefore of finding a semi-matching in a bipartite graph.  ... 
doi:10.1109/ipdpsw.2013.30 dblp:conf/ipps/BenoitLU13 fatcat:heo5gbzi3bbrvlmgjcv5cbewwi

Faster Algorithms for Semi-Matching Problems [article]

Jittat Fakcharoenphol and Bundit Laekhanukit and Danupon Nanongkai
2012 arXiv   pre-print
We consider the problem of finding semi-matching in bipartite graphs which is also extensively studied under various names in the scheduling literature.  ...  We give faster algorithms for both weighted and unweighted case.  ...  Acknowledgment We thank David Pritchard for useful suggestions, Jane (Pu) Gao for pointing out some related surveys, and Dijun Luo for pointing out some errors in the earlier version of this paper.  ... 
arXiv:1004.3363v5 fatcat:avroywzkgvdrfktxoml6g2jc3u

Efficient Load-Balancing through Distributed Token Dropping [article]

Sebastian Brandt and Barbara Keller and Joel Rybicki and Jukka Suomela and Jara Uitto
2021 arXiv   pre-print
We use the token dropping game as a tool to design an efficient distributed algorithm for stable orientations and more generally for locally optimal semi-matchings. The prior work by Czygrinow et al.  ...  We introduce a new graph problem, the token dropping game, and we show how to solve it efficiently in a distributed setting.  ...  For the balanced case ∆ = C = S, both of the algorithms run in O(∆ 5 ) rounds. The stable assignment problem is closely connected to a load balancing problem known as semi-matching [HLLT06] .  ... 
arXiv:2005.07761v2 fatcat:jd23kqhrsvbfvokhrnaaxpkr6y
« Previous Showing results 1 — 15 out of 1,184 results