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A fast greedy sequential heuristic for the vertex colouring problem based on bitwise operations

Larisa Komosko, Mikhail Batsyn, Pablo San Segundo, Panos M. Pardalos
2015 Journal of combinatorial optimization  
The suggested algorithm builds the same colouring of the graph as the well-known greedy sequential heuristic in which on every step the current vertex is coloured in the minimum possible colour.  ...  Our main contributions include introduction of a special matrix of forbidden colours and application of efficient bitwise operations on bit representations of the adjacency and forbidden colours matrices  ...  Acknowledgments The work is conducted at National Research University Higher School of Economics and supported by RSF Grant 14-41-00039.  ... 
doi:10.1007/s10878-015-9862-1 fatcat:omlb3zqzzbfd5gwpik5lngw3eu

Page 805 of Mathematical Reviews Vol. , Issue 82b [page]

1982 Mathematical Reviews  
Authors’ summary: “Many heuristic polynomial time algorithms exist to colour the vertices of connected undirected graphs having no loops or multiple edges.  ...  Associated with each such algorithm are graphs for which the number of colours required in the colouring produced by the algorithm is significantly greater than the minimum that are necessary.  ... 

An analysis of the graph processing landscape

Miguel E. Coimbra, Alexandre P. Francisco, Luís Veiga
2021 Journal of Big Data  
For these systems focused on processing the bulk of graph elements, common use-cases consist in executing for example algorithms for vertex ranking or community detection, which produce insights on graph  ...  For the use-case of performing global computations over a graph, it is first ingested into a graph processing system from one of many digital representations.  ...  The authors note that common colouring algorithms may suffer from low parallelism due to a large number of colours being needed to process large graphs with billions of vertices.  ... 
doi:10.1186/s40537-021-00443-9 pmid:33850687 pmcid:PMC8033100 fatcat:vnwcn2pwszhv3detnwcv6jrthu

Fast parallel algorithm to the minimum edge cover problem based on DNA molecular computation

Zhaocai Wang, Dongmei Huang, Chengpei Tang
2013 Applied Mathematics & Information Sciences  
vertices or edges solutions result, such as the minimum edge cover problem, graph colouring problem and so on.  ...  For an undirected and simple graph with n vertices and m edges, we reasonably design fixed length DNA strands representing vertices and edges of the graph, take appropriate steps and get the solutions  ...  The authors are grateful to the anonymous referee for a careful checking of the details and for helpful comments that improved this paper.  ... 
doi:10.12785/amis/072l48 fatcat:y5wqcmjjvfalte3qrgzpjwjm7y

BDD-Based Algorithm for SCC Decomposition of Edge-Coloured Graphs [article]

Nikola Beneš, Luboš Brim, Samuel Pastva, David Šafránek
2022 arXiv   pre-print
The large number of vertices prevents us from analysing such graphs using explicit SCC detection algorithms, such as Tarjan's, which motivates the use of a symbolic approach.  ...  The size of edge-coloured graphs appearing in practice can be enormous both in the number of vertices and colours.  ...  In [BBB + 17, BBP + 19] we have initially attacked the SCC decomposition problem for massive edge-coloured graphs by developing a parallel, semi-symbolic algorithm for detection of bottom SCCs.  ... 
arXiv:2108.13113v3 fatcat:hblyf6tm4fbzvk6un3b5ka5i6y

A complete resolution of the Keller maximum clique problem [chapter]

Jennifer Debroni, John D. Eblen, Michael A. Langston, Wendy Myrvold, Peter Shor, Dinesh Weerapurage
2011 Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms  
Keller graphs are in the benchmark set of clique problems from the DIMACS clique challenge, and they appear to be especially difficult for clique algorithms.  ...  A d-dimensional Keller graph has vertices which are numbered with each of the 4 d possible d-digit numbers (d-tuples) which have each digit equal to 0, 1, 2, or 3.  ...  A specific colouring of the Keller graph vertices is exploited by the clique algorithm. Understanding this colouring is critical for verification of the isomorphism screening described in Section 6.  ... 
doi:10.1137/1.9781611973082.11 dblp:conf/soda/DebroniELMSW11 fatcat:g7o42lagwzasffyh4te2et5eca

Benchmarking of Graph Partitioning Tools and Techniques

2019 International journal of recent technology and engineering  
In this paper the authors have used a systematic literature review to provide benchmarking on influencing parameters for graph partitioning tools, which is the principal contribution of the present paper  ...  Also authors have suggested future research directions and anomalies for improvement in tools and techniques for Graph Partitioning.  ...  Features:  Mainly used by data analysts and scientists intense to discover and distinguish graphs.  It is similar Photoshop tool but used for graph data through representation, manipulation of data,  ... 
doi:10.35940/ijrte.d7369.118419 fatcat:hy2qdjhk6zbd5al5up26qce7yy

Optimal parallel algorithms on planar graphs

Torben Hagerup
1990 Information and Computation  
Few existing parallel graph algorithms achieve optimality when applied to very sparse graphs such as planar graphs.  ...  It has been known for some time that for graphs with n vertices and m edges, all of the above problems can be solved in O(log n) time on a CRCW PRAM with O(n + m) processors.  ...  Then let I= 0 and step through the set of new colours, for each colour simultaneously adding to I all vertices of that colour that have no neighbours in I.  ... 
doi:10.1016/0890-5401(90)90034-f fatcat:w3zm46mljvh73cqhrctew5ukfi

Bitboard Methods for Games

Cameron Browne
2014 ICGA Journal  
Bitboards allow the efficient encoding of games for computer play and the application of fast bitwiseparallel algorithms for common game-related operations.  ...  , and (3) a sampling of bitboard algorithms for a range of games other than chess, with notes on their performance and practical application.  ...  Flip Updates Algorithm 9 shows a bitwise-parallel algorithm for flipping all adjacent enemy pieces to a player's colour.  ... 
doi:10.3233/icg-2014-37202 fatcat:vbb63uxs4je5dnwr33l5qugsli

Quantum inspired cuckoo search algorithm for graph colouring problem

Halima Djelloul, Abdesslem Layeb, Salim Chikhi
2015 International Journal of Bio-Inspired Computation (IJBIC)  
In this paper, we try to solve the graph coloring problem using a new approach based on the quantum inspired cuckoo search algorithm.  ...  To show the feasibility and the effectiveness of the algorithm, we have used the standard DIMACS benchmark, and the obtained results are very encouraging.  ...  In the initialization step, the developed algorithm called QICSACOL (Quantum Inspired Cuckoo Search Algorithm for Graph COLoring), generates the initial population of nests by using the RLF algorithm  ... 
doi:10.1504/ijbic.2015.069554 fatcat:urza3pid7fdvxfo7an2j5hrsbu

A Complete Graphical Calculus for Spekkens' Toy Bit Theory

Miriam Backens, Ali Nabi Duman
2015 Foundations of physics  
These models are also used to explore the question of ψ-ontic versus ψ-epistemic theories for quantum mechanics. Spekkens' toy theory is one such model.  ...  Thus Spekkens' toy bit theory and stabilizer quantum mechanics can be analysed and compared using analogous graphical formalisms.  ...  Acknowledgements The authors would like to thank Dominic Horsman and Matt Pusey for comments on drafts of this paper. MB acknowledges financial support from the EPSRC.  ... 
doi:10.1007/s10701-015-9957-7 fatcat:vtnfcnci6bdkdniwdlznmx6ymu

A Parallel Quantum Histogram Architecture

G. M. Megson, J. O. Cadenas, R. S. Sherratt, P. Huerta, W. C. Kao
2013 IEEE Transactions on Circuits and Systems - II - Express Briefs  
A parallel formulation of an algorithm for the histogram computation of n data items using an on-the-fly data decomposition and a novel quantum-like representation (QR) is developed.  ...  Index Terms-Histogram, parallel architectures, parallel algorithms, quantum representation. G. M. Megson is with the  ...  As a result of the consequent reformulation and manipulation of the algorithm, the internal structure of the cells is simplified compared to [3, 4] and consequently array architectures for processing  ... 
doi:10.1109/tcsii.2013.2258263 fatcat:hhuleaahyfgaxkbvcwvbjtgswi

Fast Computation of Small Cuts via Cycle Space Sampling [article]

David Pritchard, Ramakrishna Thurimella
2010 arXiv   pre-print
In the model of distributed computing in a graph G=(V, E) with O(log V)-bit messages, our approach yields faster algorithms for several problems.  ...  This leads to simple new linear-time sequential algorithms for finding all cut edges and cut pairs (a set of 2 edges that form a cut) of a graph.  ...  Alg. for valuable feedback.  ... 
arXiv:cs/0702113v5 fatcat:stbkbsbpdncbbaeeircnzcdfwa

Janus: An FPGA-Based System for High-Performance Scientific Computing

F. Belletti, M. Cotallo, A. Cruz, L.A. Fernandez, A. Gordillo-Guerrero, M. Guidetti, A. Maiorano, F. Mantovani, E. Marinari, V. Martin-Mayor, A. Muoz-Sudupe, D. Navarro (+11 others)
2009 Computing in science & engineering (Print)  
JANUS is tailored for, but not limited to, the requirements of a class of hard scientific applications characterized by regular code structure, unconventional data manipulation instructions and not too  ...  We discuss the architecture of this configurable machine, and focus on its use on Monte Carlo simulations of statistical mechanics.  ...  Sialino for their outstanding support during the commissioning of the first JANUS system.  ... 
doi:10.1109/mcse.2009.11 fatcat:uy6fojv45jcslf5pkgjzzoikmq

CytoASP: a Cytoscape app for qualitative consistency reasoning, prediction and repair in biological networks

Aristotelis Kittas, Amélie Barozet, Jekaterina Sereshti, Niels Grabe, Sophia Tsoka
2015 BMC Systems Biology  
Results: We report the implementation of CytoASP, an app that allows the use of BioASP for influence graph consistency checking, prediction and repair operations through Cytoscape.  ...  Conclusion: We have presented a user-friendly Cytoscape app for the analysis of regulatory networks using BioASP.  ...  The software takes advantage of the extensive BioASP functionality in manipulating influence graphs, allowing for the modelling of large scale regulatory networks and dealing with inconsistency with extensive  ... 
doi:10.1186/s12918-015-0179-6 pmid:26163265 pmcid:PMC4499222 fatcat:dj2jhvwgrvcifamqb7j37gfeoi
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