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Near approximation of maximum weight matching through efficient weight reduction [article]

Andrzej Lingas, Cui Di
2011 arXiv   pre-print
We show that if we can approximate a maximum weight matching in G within factor alpha in time T(n,m,W) then we can find a matching of weight at least (alpha-epsilon) times the maximum weight of a matching  ...  In particular, if we combine our result with the recent (1-\epsilon)-approximation algorithm for maximum weight matching in graphs due to Duan and Pettie whose time complexity has a poly-logarithmic dependence  ...  Acknowledgments The authors are very grateful to Seth Pettie for his valuable suggestions to apply the second (1 − ǫ)-approximation algorithm from [7] instead of the first one and to eliminate an n log  ... 
arXiv:1012.5911v2 fatcat:ybhxs7q5vvcy5kqde42geeszwe

Boosting Data Reduction for the Maximum Weight Independent Set Problem Using Increasing Transformations [article]

Alexander Gellner, Sebastian Lamm, Christian Schulz, Darren Strash, Bogdán Zaválnij
2020 arXiv   pre-print
Given a vertex-weighted graph, the maximum weight independent set problem asks for a pair-wise non-adjacent set of vertices such that the sum of their weights is maximum.  ...  We introduce new generalized data reduction and transformation rules for the problem. A key feature of our work is that some transformation rules can increase the size of the input.  ...  Let I be a maximum weight independent set in G and α w (G ) its weight.  ... 
arXiv:2008.05180v2 fatcat:il2uanigjrgj5p6nqkvtuuvtje

Near Approximation of Maximum Weight Matching through Efficient Weight Reduction [chapter]

Andrzej Lingas, Cui Di
2011 Lecture Notes in Computer Science  
We show that if we can approximate a maximum weight matching in G within factor α in time T (n, m, W ) then we can find a matching of weight at least (α − ǫ) times the maximum weight of a matching in G  ...  in time In particular, if we combine our result with the recent (1 − ǫ)-approximation algorithm for maximum weight matching in graphs with small edge weights due to Duan and Pettie then we obtain (1 −  ...  Acknowledgments The authors are grateful to anonymous referees for valuable comments on a preliminary version of the paper.  ... 
doi:10.1007/978-3-642-20877-5_6 fatcat:jd5e7wdhkbhwldraw5furxxeli

Instantly decodable network coding for real-time device-to-device communications

Ahmed Douik, Sameh Sorour, Tareq Y. Al-Naffouri, Mohamed-Slim Alouini
2016 EURASIP Journal on Advances in Signal Processing  
Due to the complexity of discovering such maximum clique, the paper presents a fast selection algorithm.  ...  The complexity of the solution is reduced by first proposing efficient methods for the construction, the update, and the dimension reduction of the IDNC graph.  ...  This paper proposes to reduce the complexity of the delay reduction algorithms through efficient construction, update, and dimension reduction of the solution.  ... 
doi:10.1186/s13634-015-0293-z fatcat:xoqmm7sfdnhmvct7cjxkwgycfq

Recent Advances in Practical Data Reduction [article]

Faisal Abu-Khzam, Sebastian Lamm, Matthias Mnich, Alexander Noe, Christian Schulz, Darren Strash
2020 arXiv   pre-print
Over the last two decades, significant advances have been made in the design and analysis of fixed-parameter algorithms for a wide variety of graph-theoretic problems.  ...  We survey recent trends in data reduction engineering results for selected problems.  ...  Partially supported by DFG grants MN 59/1-1 and SCHU 2567/1-2.  ... 
arXiv:2012.12594v3 fatcat:vpsucno5cvgotovfiihkyyytba

Page 467 of Mathematical Reviews Vol. , Issue 88a [page]

1988 Mathematical Reviews  
Summary: “Parallel algorithms are given for finding a maximum weighted clique, a maximum weighted independent set, a minimum clique cover, and a minimum weighted dominating set of an inter- val graph.  ...  Diana Schmidt (Karlsruhe) 88a:68043 68Q20 05C35 68R10 Alon, Noga (1-MIT); Babai, Laszl6 (1-CHI); Itai, Alon (1-CHI) A fast and simple randomized parallel algorithm for the maximal independent set problem  ... 

Fast and simple approximation algorithms for maximum weighted independent set of links

Peng-Jun Wan, Xiaohua Jia, Guojun Dai, Hongwei Du, Ophir Frieder
2014 IEEE INFOCOM 2014 - IEEE Conference on Computer Communications  
Finding a maximum-weighted independent set of links is a fundamental problem in wireless networking and has broad applications in various wireless link scheduling problems.  ...  In this paper, we present a number of fast and simple approximation algorithms under the general protocol interference model.  ...  Given a subset of and a positive weight function on , the problem of finding an independent subset (abbreviated with IS) of with maximum total weight ∑ ∈ ( ) is known as Maximum Weighted Independent Set  ... 
doi:10.1109/infocom.2014.6848102 dblp:conf/infocom/WanJDDF14 fatcat:fd7jdo2lwrbufag4c4czkrdvie

Towards Nearly-Linear Time Algorithms for Submodular Maximization with a Matroid Constraint

Alina Ene, Huy L. Nguyen, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
We develop a new algorithm for a general matroid constraint with a 1 − 1/e − approximation that achieves a fast running time provided we have a fast data structure for maintaining an approximately maximum  ...  weight base in the matroid through a sequence of decrease weight operations.  ...  Suppose that we have a data structure for maintaining a maximum weight base and independent set as described above.  ... 
doi:10.4230/lipics.icalp.2019.54 dblp:conf/icalp/EneN19a fatcat:ctcnzhg3zzgdfb6l5mpw7ffvw4

Parallel computation on interval graphs using PC clusters: Algorithms and experiments [chapter]

A. Ferreira, I. Guérin Lassous, K. Marcus, A. Rau-Chaplin
1998 Lecture Notes in Computer Science  
interval covering, maximum independent set and minimum dominating set.  ...  on a Fast Ethernet based PC cluster.  ...  In the maximum weighted clique problem for an interval graph, we want to know the maximum weight of such a set, given weights p(I 0 > 0 on the intervals, and identify a maximum weighted clique by marking  ... 
doi:10.1007/bfb0057943 fatcat:2lltogfmgrelfpyvmlw22r2yhy

Scalable Graph Algorithms [article]

Christian Schulz
2019 arXiv   pre-print
Designing and evaluating scalable graph algorithms to handle these data sets is a crucial task on the road to understanding the underlying systems.  ...  This habilitation thesis is a summary a broad spectrum of scalable graph algorithms that I developed over the last six years with many coauthors.  ...  Such a set is called a maximum weight independent set (MWIS).  ... 
arXiv:1912.00245v1 fatcat:mop2e6pqtnbr7irkrakraael6a

Matching is as easy as matrix inversion

Ketan Mulmuley, Umesh V. Vazirani, Vijay V. Vazirani
1987 Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87  
We show applications of this lemma to parallel computation and randomized reductions.  ...  A new algorithm for finding a maximum matching in a general graph is presented; its special feature being that the only computationally non-trivial step required in its execution is the inversion of a  ...  The reduction is as follows. First assign a random and independent weight w(v) to each vertex VEV, chosen from [l, 2n1, where n = IVI.  ... 
doi:10.1145/28395.383347 dblp:conf/stoc/MulmuleyVV87 fatcat:jupztmizqfdzpjsvcatu37roqi

Matching is as easy as matrix inversion

Ketan Mulmuley, Umesh V. Vazirani, Vijay V. Vazirani
1987 Combinatorica  
We show applications of this lemma to parallel computation and randomized reductions.  ...  A new algorithm for finding a maximum matching in a general graph is presented; its special feature being that the only computationally non-trivial step required in its execution is the inversion of a  ...  The reduction is as follows. First assign a random and independent weight w(v) to each vertex VEV, chosen from [l, 2n1, where n = IVI.  ... 
doi:10.1007/bf02579206 fatcat:a6qd6xuqcbhufgqnk2sn4vyesa

On complexity of optimized crossover for binary representations [article]

Anton Eremeev
2007 arXiv   pre-print
We study a connection between the OGTC for linear Boolean programming problem and the maximum weight independent set problem on 2-colorable hypergraph and prove the NP-hardness of several special cases  ...  By means of efficient reductions of the optimized gene transmitting crossover problems (OGTC) we show the polynomial solvability of the OGTC for the maximum weight set packing problem, the minimum weight  ...  This simplified reduction is identical to the one in Proposition 1 if A is an incidence matrix of the ordinary graph G given for the maximum weight independent set problem and b = e.  ... 
arXiv:0705.3766v1 fatcat:xhprpsxg75gs7p73ry3xnow7ze

A fast CU Size Decision Algorithm for 3D-HEVC

Yubing Wang, Yongfang Wang, Yawen Shi, S.A. Hamouda, M. Mirzaei, Z. Yu
2016 MATEC Web of Conferences  
To speed up the encoding process for the dependent texture views, we propose a fast CU depth range selection algorithm by jointly making use of the inter-view and temporal-spatial correlations.  ...  Firstly, adaptive correlation weights are proposed to predict coding unit(CU) depth range and skip some specific depth levels rarely used in independent view, the previous frame and neighboring CUs.  ...  Based on the characteristics of 3D video, we propose a depth range selection algorithm based on adaptive weights using split complexity(SC), which is defined as follows: is the maximum value of depth level  ... 
doi:10.1051/matecconf/20166107006 fatcat:shtoegnnfzhkjivs4tsnz5jcie

The maximum clique problem

Panos M. Pardalos, Jue Xue
1994 Journal of Global Optimization  
In this paper we present a survey of results concerning algorithms, complexity, and applications of the maximum clique problem.  ...  We discuss enumerative and exact algorithms, heuristics, and a variety of other proposed methods. An up to date bibliography on the maximum clique and related problems is also provided.  ...  The size of a maximum independent set is the stability number of G (denoted by a(G)). The maximum weight independent set problem asks for an independent set of maximum weight.  ... 
doi:10.1007/bf01098364 fatcat:qmknkbopunaijoi7joaaab3rey
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