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An Efficient Algorithm for the Nearly Equitable Edge Coloring Problem

Xuzhen Xie, Mutsunori Yagiura, Takao Ono, Tomio Hirata, Uri Zwick
2008 Journal of Graph Algorithms and Applications  
An edge coloring of a multigraph is nearly equitable if, among the edges incident to each vertex, the numbers of edges colored with any two colors differ by at most two.  ...  a constructive proof for the existence of a nearly equitable edge coloring for any multigraph.  ...  Acknowledgments The authors wish to thank the referees for several valuable comments and useful suggestions.  ... 
doi:10.7155/jgaa.00171 fatcat:pcxxqpgwy5brxotj2sze5pybmy

A Fast Algorithm for Computing a Nearly Equitable Edge Coloring with Balanced Conditions

Akiyoshi Shioura, Mutsunori Yagiura
2010 Journal of Graph Algorithms and Applications  
We discuss the nearly equitable edge coloring problem on a multigraph and propose an efficient algorithm for solving the problem, which has a better time complexity than the previous algorithms.  ...  The coloring computed by our algorithm satisfies additional balanced conditions on the number of edges used in each color class, where conditions are imposed on the balance among all edges in the multigraph  ...  Table 1 shows a summary of the previous algorithms for the nearly equitable edge coloring problem.  ... 
doi:10.7155/jgaa.00213 fatcat:ydwn437gpjdctkj5to555ri3uy

A Fast Algorithm for Computing a Nearly Equitable Edge Coloring with Balanced Conditions [chapter]

Akiyoshi Shioura, Mutsunori Yagiura
2009 Lecture Notes in Computer Science  
We discuss the nearly equitable edge coloring problem on a multigraph and propose an efficient algorithm for solving the problem, which has a better time complexity than the previous algorithms.  ...  The coloring computed by our algorithm satisfies additional balanced conditions on the number of edges used in each color class, where conditions are imposed on the balance among all edges in the multigraph  ...  Table 1 shows a summary of the previous algorithms for the nearly equitable edge coloring problem.  ... 
doi:10.1007/978-3-642-02882-3_13 fatcat:735o36ke2jc7tlwkoq6mtt7uni

Equitable Coloring of Graphs. Recent Theoretical Results and New Practical Algorithms

Hanna Furmańczyk, Andrzej Jastrzębski, Marek Kubale
2016 Archives of Control Sciences  
Next, since the general coloring problem is strongly NP-hard, we report on practical experiments with some efficient polynomial-time algorithms for approximate equitable coloring of general graphs.  ...  In this paper we survey recent theoretical results concerning conditions for equitable colorability of some graphs and recent theoretical results concerning the complexity of equitable coloring problem  ...  They proved the following Ore-type theorem. Theorem 3 [20] Every graph satisfying deg(x) + deg(y) 2r + 1 for every edge {x, y}, has an equitable (r + 1)-coloring.  ... 
doi:10.1515/acsc-2016-0016 fatcat:pqjhgc3up5dwpowixzd4hxrqrq

Optimal transceiver scheduling in WDM/TDM networks

R. Berry, E. Modiano
2005 IEEE Journal on Selected Areas in Communications  
We establish a relationship between this problem and edge colorings of graphs which are determined by the offered traffic.  ...  We then develop a heuristic algorithm for general traffic that uses nearly the minimum number of transceivers.  ...  Next we discuss an efficient (polynomial time) algorithm for finding this solution.  ... 
doi:10.1109/jsac.2005.852240 fatcat:r4sjn5nmhjcwdpkxndoubd2dcy

Graph Iso/Auto-morphism: A Divide- -Conquer Approach [article]

Can Lu, Jeffrey Xu Yu, Zhiwei Zhang, Hong Cheng
2019 arXiv   pre-print
A closely related problem is automorphism detection, where an isomorphism between two graphs is a bijection between their vertex sets that preserves adjacency, and an automorphism is an isomorphism from  ...  The canonical labeling for a tree node can be obtained by the canonical labeling of its child nodes, and the canonical labeling for the root is the one for G.  ...  The refinement function R: For every tree node with a sequence ν (the edge-label sequence from the root to the node), the refinement function, R : G × Π × V * → Π, specifies an equitable coloring corresponding  ... 
arXiv:1911.06511v1 fatcat:z42uz5wzbvhjhc6fdjrphjr4dy

Equitable (d,m)-edge designs [article]

Jean-Marc Fédou, Maria João Rendas
2013 arXiv   pre-print
We give constructive procedures for completing the definition of the clustered designs proposed Morris 1991, that become defined for arbitrary number of input factors and desired clusters' multiplicity  ...  The paper addresses design of experiments for classifying the input factors of a multi-variate function into negligible, linear and other (non-linear/interaction) factors.  ...  The number m i of edges of S ⊂ Q d having color i satisfies < P S , X i P S >= 2m i , i ∈ {1, . . . , d} . (5) Problem (re)formulation Denote by E d m the set of (d, m)-edge equitable polynomials.  ... 
arXiv:1307.1996v1 fatcat:y2vsepokknfbpf22kees6kc3fq

Efficient Distributed Computation of MIS and Generalized MIS in Linear Hypergraphs [article]

Fabian Kuhn, Chaodong Zheng
2018 arXiv   pre-print
We first present a randomized algorithm for computing an MIS in linear hypergraphs. It has poly-logarithmic runtime and it works in the CONGEST model.  ...  Finding an MIS is a fundamental problem in distributed computing.  ...  Efficient computation of an MIS is an important problem in distributed computing theory: it is a fundamental symmetry breaking problem; it could also be a key building block for solving many other problems  ... 
arXiv:1805.03357v1 fatcat:eorfvfxvbjairi5lr47on2c3oi

The Algorithmic Aspects of the Regularity Lemma

N. Alon, R.A. Duke, H. Lefmann, V. Rodl, R. Yuster
1994 Journal of Algorithms  
coloring problems. * Part of this paper was presented at the 33 rd  ...  constructive version of the Regularity Lemma supplies efficient sequential and parallel algorithms for many problems, some of which are naturally motivated by the study of various graph embedding and graph  ...  The algorithm can be parallelized and supplies efficient sequential and parallel algorithms for many problems.  ... 
doi:10.1006/jagm.1994.1005 fatcat:ww5ewrsbabf2daj7jge4llf5e4

The algorithmic aspects of the regularity lemma

N. Alon
1992 Proceedings., 33rd Annual Symposium on Foundations of Computer Science  
coloring problems. * Part of this paper was presented at the 33 rd  ...  constructive version of the Regularity Lemma supplies efficient sequential and parallel algorithms for many problems, some of which are naturally motivated by the study of various graph embedding and graph  ...  The algorithm can be parallelized and supplies efficient sequential and parallel algorithms for many problems.  ... 
doi:10.1109/sfcs.1992.267804 dblp:conf/focs/AlonDLRY92 fatcat:rx64anvblzed7ji4kh6e43nyvi

GAEA: Graph Augmentation for Equitable Access via Reinforcement Learning [article]

Govardana Sachithanandam Ramachandran, Ivan Brugere, Lav R. Varshney, Caiming Xiong
2021 arXiv   pre-print
Here we introduce a new class of problems, Graph Augmentation for Equitable Access (GAEA), to enhance equity in networked systems by editing graph edges under budget constraints.  ...  We further demonstrate the method on real-world networks, by merging public census, school, and transportation datasets for the city of Chicago and applying our algorithm to find human-interpretable edits  ...  However, on the low-degree problem instance, our method nearly doubles the utility performance of the baseline.  ... 
arXiv:2012.03900v2 fatcat:xnotbuzozbedrf4ahuba4bubra

Integrated Crossover Based Evolutionary Algorithm for Coloring Vertex-Weighted Graphs

Betul Boz, Gizem Sungu
2020 IEEE Access  
INDEX TERMS Graph coloring problem, vertex-weighted graphs, crossover operator, evolutionary algorithms, k-coloring.  ...  Graph coloring is one of the main optimization problems widely studied in the literature.  ...  ACKNOWLEDGMENT This article [47] was presented in part at the Genetic and Evolutionary Computation Conference (GECCO'15), Madrid, Spain, in 2015.  ... 
doi:10.1109/access.2020.3008886 fatcat:z4zh345qbrgedbjm7e3pwjwngq

Parameterized Complexity of Envy-Free Resource Allocation in Social Networks

Eduard Eiben, Robert Ganian, Thekla Hamm, Sebastian Ordyniak
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We consider the classical problem of allocating resources among agents in an envy-free (and, where applicable, proportional) way.  ...  We initiate the study of the parameterized complexity of these resource allocation problems by considering natural parameters which capture structural properties of the network and similarities between  ...  Robert Ganian and Thekla Hamm acknowledge support from the Austrian Science Fund (FWF, Project P31336: NFPC). Thekla Hamm is co-funded by FWF project W1255-N23.  ... 
doi:10.1609/aaai.v34i05.6201 fatcat:3rqotjmdoje4lp7twamg6d3pna

Expanding the Expressive Power of Monadic Second-Order Logic on Restricted Graph Classes [chapter]

Robert Ganian, Jan Obdržálek
2013 Lecture Notes in Computer Science  
This raises the following, crucial question: would it be possible to naturally extend the language of MSO 1 to include additional well-studied problems without sacrificing the positive algorithmic results  ...  Vertex cover has been generally used to solve individual problems for which traditional width parameters fail to help (see e.g. [1, 6, 9, 10] ).  ...  Equitable c-coloring [18] is probably the most extensively studied example of an equitable problem.  ... 
doi:10.1007/978-3-642-45278-9_15 fatcat:xhfihylucrglzgzwwsax4usoj4

Revealing Structure in Large Graphs: Szemerédi's Regularity Lemma and its Use in Pattern Recognition [article]

Marcello Pelillo, Ismail Elezi, Marco Fiorucci
2016 arXiv   pre-print
In this paper we will provide an overview of the regularity lemma and its algorithmic aspects, and will discuss its relevance in the context of pattern recognition research.  ...  Introduced in the mid-1970's as an intermediate step in proving a long-standing conjecture on arithmetic progressions, Szemer\'edi's regularity lemma has emerged over time as a fundamental tool in different  ...  Bazsó for reading a preliminary version of the paper, and to the anonymous reviewers for their constructive feedback.  ... 
arXiv:1609.06583v1 fatcat:ci24pl24y5ax5dujr4tjmf75xy
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