The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Kertas kerja ini membentangkan algoritma pewarnaan graf heuristik yang dinamakan MIPS_CLR, algoritma Carian Pemprosesan keadaan MInimal untuk masalah CoLoRing graf. Diberi graf G(V, E), matlamat masalah NP-lengkap ini adalah untuk mencari penetapan warna pada setiap bucu masuk V supaya mana-mana pasangan bucu bersebelahan tidak boleh menerima warna yang sama tetapi juga jumlah bilangan warna harus diminimumkan. Masalah pewarnaan graf telah dikaji secara meluas kerana bilangan aplikasi praktikalnya yang banyak dalam pelbagai bidang. Dalam MIPS_CLR, peringkat pembinaan mula-mula menghasilkan keadaan minimum awal yang terdiri daripada sebanyak bucu berwarna oleh algoritma tamak mudah, selepas kumpulan maksimum G ditemui oleh algoritma klik maksimum. Kemudian, peringkat penghalusan secara berulang mencari keadaan penyelesaian sambil mengekalkan keminimuman dari segi fungsi kos dengan kaedah peralihan keadaan minimum. Dalam kaedah ini, skema pemilihan warna terbaik, pemilihan warna rawak, shuffle penetapan warna dan pengembangan warna secara beransur-ansur digunakan bersama-sama untuk merealisasikan carian turunan diskret dengan keupayaan mendaki bukit. Prestasi MIPS_CLR dinilai melalui penyelesaian kejadian graf penanda aras DIMACS, di mana kualiti penyelesaian umumnya lebih baik daripada algoritma sedia ada manakala masa pengiraan adalah setanding dengan algoritma sedia ada yang terbaik. Khususnya, MIPS_CLR menyediakan penyelesaian sempadan bawah baharu untuk beberapa keadaan. Hasil simulasi mengesahkan keupayaan carian meluas pendekatan MIPS_CLR kami untuk masalah pewarnaan graf.
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Salinan
Nobuo FUNABIKI, Teruo HIGASHINO, "A Minimal-State Processing Search Algorithm for Graph Coloring Problems" in IEICE TRANSACTIONS on Fundamentals,
vol. E83-A, no. 7, pp. 1420-1430, July 2000, doi: .
Abstract: This paper presents a heuristic graph coloring algorithm named MIPS_CLR, a MInimal-state Processing Search algorithm for the graph CoLoRing problem. Given a graph G(V, E), the goal of this NP-complete problem is to find a color assignment to every vertex in V such that any pair of adjacent vertices must not receive the same color but also the total number of colors should be minimized. The graph coloring problem has been widely studied due to its large number of practical applications in various fields. In MIPS_CLR, a construction stage first generates an initial minimal state composed of as many as colored vertices by a simple greedy algorithm, after a maximal clique of G is found by a maximum clique algorithm. Then, a refinement stage iteratively seeks a solution state while keeping minimality in terms of a cost function by a minimal-state transition method. In this method, the schemes of a best color selection, a random color selection, a color assignment shuffle, and a gradual color expansion are used together to realize the discrete descent search with hill-climbing capabilities. The performance of MIPS_CLR is evaluated through solving DIMACS benchmark graph instances, where the solution quality is generally better than existing algorithms while the computation time is comparable with the best existing one. In particular, MIPS_CLR provides new lower bound solutions for several instances. The simulation results confirm the extensive search capability of our MIPS_CLR approach for the graph coloring problem.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e83-a_7_1420/_p
Salinan
@ARTICLE{e83-a_7_1420,
author={Nobuo FUNABIKI, Teruo HIGASHINO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Minimal-State Processing Search Algorithm for Graph Coloring Problems},
year={2000},
volume={E83-A},
number={7},
pages={1420-1430},
abstract={This paper presents a heuristic graph coloring algorithm named MIPS_CLR, a MInimal-state Processing Search algorithm for the graph CoLoRing problem. Given a graph G(V, E), the goal of this NP-complete problem is to find a color assignment to every vertex in V such that any pair of adjacent vertices must not receive the same color but also the total number of colors should be minimized. The graph coloring problem has been widely studied due to its large number of practical applications in various fields. In MIPS_CLR, a construction stage first generates an initial minimal state composed of as many as colored vertices by a simple greedy algorithm, after a maximal clique of G is found by a maximum clique algorithm. Then, a refinement stage iteratively seeks a solution state while keeping minimality in terms of a cost function by a minimal-state transition method. In this method, the schemes of a best color selection, a random color selection, a color assignment shuffle, and a gradual color expansion are used together to realize the discrete descent search with hill-climbing capabilities. The performance of MIPS_CLR is evaluated through solving DIMACS benchmark graph instances, where the solution quality is generally better than existing algorithms while the computation time is comparable with the best existing one. In particular, MIPS_CLR provides new lower bound solutions for several instances. The simulation results confirm the extensive search capability of our MIPS_CLR approach for the graph coloring problem.},
keywords={},
doi={},
ISSN={},
month={July},}
Salinan
TY - JOUR
TI - A Minimal-State Processing Search Algorithm for Graph Coloring Problems
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1420
EP - 1430
AU - Nobuo FUNABIKI
AU - Teruo HIGASHINO
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E83-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2000
AB - This paper presents a heuristic graph coloring algorithm named MIPS_CLR, a MInimal-state Processing Search algorithm for the graph CoLoRing problem. Given a graph G(V, E), the goal of this NP-complete problem is to find a color assignment to every vertex in V such that any pair of adjacent vertices must not receive the same color but also the total number of colors should be minimized. The graph coloring problem has been widely studied due to its large number of practical applications in various fields. In MIPS_CLR, a construction stage first generates an initial minimal state composed of as many as colored vertices by a simple greedy algorithm, after a maximal clique of G is found by a maximum clique algorithm. Then, a refinement stage iteratively seeks a solution state while keeping minimality in terms of a cost function by a minimal-state transition method. In this method, the schemes of a best color selection, a random color selection, a color assignment shuffle, and a gradual color expansion are used together to realize the discrete descent search with hill-climbing capabilities. The performance of MIPS_CLR is evaluated through solving DIMACS benchmark graph instances, where the solution quality is generally better than existing algorithms while the computation time is comparable with the best existing one. In particular, MIPS_CLR provides new lower bound solutions for several instances. The simulation results confirm the extensive search capability of our MIPS_CLR approach for the graph coloring problem.
ER -