Scalable parallel graph coloring algorithms
Finding a good graph coloring quickly is often a crucial phase in the development of efficient, parallel algorithms for many scientific and engineering applications. In this paper we consider the problem of solving the graph coloring problem itself in parallel. We present a simple and fast parallel...
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Chichester, UK
John Wiley & Sons, Ltd
01.10.2000
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| Abstract | Finding a good graph coloring quickly is often a crucial phase in the development of efficient, parallel algorithms for many scientific and engineering applications. In this paper we consider the problem of solving the graph coloring problem itself in parallel. We present a simple and fast parallel graph coloring heuristic that is well suited for shared memory programming and yields an almost linear speedup on the PRAM model. We also present a second heuristic that improves on the number of colors used. The heuristics have been implemented using OpenMP. Experiments conducted on an SGI Cray Origin 2000 supercomputer using very large graphs from finite element methods and eigenvalue computations validate the theoretical run‐time analysis. Copyright © 2000 John Wiley & Sons, Ltd. |
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| AbstractList | Finding a good graph coloring quickly is often a crucial phase in the development of efficient, parallel algorithms for many scientific and engineering applications. In this paper we consider the problem of solving the graph coloring problem itself in parallel. We present a simple and fast parallel graph coloring heuristic that is well suited for shared memory programming and yields an almost linear speedup on the PRAM model. We also present a second heuristic that improves on the number of colors used. The heuristics have been implemented using OpenMP. Experiments conducted on an SGI Cray Origin 2000 supercomputer using very large graphs from finite element methods and eigenvalue computations validate the theoretical run-time analysis. Finding a good graph coloring quickly is often a crucial phase in the development of efficient, parallel algorithms for many scientific and engineering applications. In this paper we consider the problem of solving the graph coloring problem itself in parallel. We present a simple and fast parallel graph coloring heuristic that is well suited for shared memory programming and yields an almost linear speedup on the PRAM model. We also present a second heuristic that improves on the number of colors used. The heuristics have been implemented using OpenMP. Experiments conducted on an SGI Cray Origin 2000 supercomputer using very large graphs from finite element methods and eigenvalue computations validate the theoretical run‐time analysis. Copyright © 2000 John Wiley & Sons, Ltd. |
| Author | Manne, Fredrik Gebremedhin, Assefaw Hadish |
| Author_xml | – sequence: 1 givenname: Assefaw Hadish surname: Gebremedhin fullname: Gebremedhin, Assefaw Hadish email: assefaw@ii.uib.no organization: Department of Informatics, University of Bergen, N-5020 Bergen, Norway – sequence: 2 givenname: Fredrik surname: Manne fullname: Manne, Fredrik organization: Department of Informatics, University of Bergen, N-5020 Bergen, Norway |
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| Cites_doi | 10.1006/jpdc.1996.0117 10.1093/comjnl/10.1.85 10.1137/0215074 10.1109/T-VT.1986.24063 10.1109/TCS.1976.1084138 10.1137/0914041 10.1017/S0305004100051124 10.1137/0720013 10.1145/359094.359101 10.1016/0096-0551(81)90048-5 |
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| References | Luby M. A simple parallel algorithm for the maximal independent set problem. SIAM Journal on Computing 1986; 15(4):1036-1053. Chaitin GJ, Auslander M, Chandra AK, Cocke J, Hopkins ME, Markstein P. Register allocation via coloring. Computer Languages 1981; 6:47-57. Jones MT, Plassmann PE. A parallel graph coloring heuristic. SIAM Journal of Scientific Computing 1993; 14(3):654-669. Brelaz D. New methods to color the vertices of a graph. Communications of the ACM 1979; 22(4):251-256. Welsh DJA, Powell MB. An upper bound for the chromatic number of a graph and its application to timetabling problems. Computer Journal 1967; 10:85-86. Grimmet GR, McDiarmid CJH. On coloring random graphs. Mathematical Proceedings of the Cambridge Philosophical Society 1975; 77:313-324. Gjertsen Jr. RK, Jones MT, Plassman P. Parallel heuristics for improved, balanced graph colorings. Journal of Parallel and Distributed Computing 1996; 37:171-186. Garey MR, Johnson DS, So HC. An application of graph coloring to printed circuit testing. IEEE Transactions on Circuits and Systems 1976; 23:591-599. Gamst A. Some lower bounds for a class of frequency assignment problems. IEEE Transactions of Vehicular Technology 1986; 35(1):8-14. Garey MR, Johnson DS. Computers and Intractability. W. H. Freeman: New York, 1979. Coleman TF, More JJ. Estimation of sparse jacobian matrices and graph coloring problems. SIAM Journal on Numerical Analysis 1983; 20(1):187-209. 1993; 14 1976; 23 1967; 10 2000 1986; 35 1986; 15 1983; 20 1981; 6 1995 1994 1975; 77 1992 1979; 22 1996; 37 1979 1998; 1541 Allwright (10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB5) 1995 Gebremedhin (10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB17) 2000 Gamst (10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB2) 1986; 35 Chaitin (10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB3) 1981; 6 Jones (10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB9) 1993; 14 Grimmet (10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB13) 1975; 77 Culberson (10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB16) 1992 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB10 Brelaz (10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB12) 1979; 22 Garey (10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB4) 1976; 23 Gjertsen Jr. (10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB15) 1996; 37 Welsh (10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB11) 1967; 10 Garey (10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB7) 1979 Manne (10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB8) 1998; 1541 Coleman (10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB6) 1983; 20 Luby (10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB14) 1986; 15 Lewandowski (10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB1) 1994 |
| References_xml | – reference: Brelaz D. New methods to color the vertices of a graph. Communications of the ACM 1979; 22(4):251-256. – reference: Jones MT, Plassmann PE. A parallel graph coloring heuristic. SIAM Journal of Scientific Computing 1993; 14(3):654-669. – reference: Welsh DJA, Powell MB. An upper bound for the chromatic number of a graph and its application to timetabling problems. Computer Journal 1967; 10:85-86. – reference: Gjertsen Jr. RK, Jones MT, Plassman P. Parallel heuristics for improved, balanced graph colorings. Journal of Parallel and Distributed Computing 1996; 37:171-186. – reference: Grimmet GR, McDiarmid CJH. On coloring random graphs. Mathematical Proceedings of the Cambridge Philosophical Society 1975; 77:313-324. – reference: Coleman TF, More JJ. Estimation of sparse jacobian matrices and graph coloring problems. SIAM Journal on Numerical Analysis 1983; 20(1):187-209. – reference: Luby M. A simple parallel algorithm for the maximal independent set problem. SIAM Journal on Computing 1986; 15(4):1036-1053. – reference: Gamst A. Some lower bounds for a class of frequency assignment problems. IEEE Transactions of Vehicular Technology 1986; 35(1):8-14. – reference: Garey MR, Johnson DS. Computers and Intractability. W. H. Freeman: New York, 1979. – reference: Chaitin GJ, Auslander M, Chandra AK, Cocke J, Hopkins ME, Markstein P. Register allocation via coloring. Computer Languages 1981; 6:47-57. – reference: Garey MR, Johnson DS, So HC. An application of graph coloring to printed circuit testing. IEEE Transactions on Circuits and Systems 1976; 23:591-599. – volume: 37 start-page: 171 year: 1996 end-page: 186 article-title: Parallel heuristics for improved, balanced graph colorings publication-title: Journal of Parallel and Distributed Computing – volume: 10 start-page: 85 year: 1967 end-page: 86 article-title: An upper bound for the chromatic number of a graph and its application to timetabling problems publication-title: Computer Journal – volume: 14 start-page: 654 issue: 3 year: 1993 end-page: 669 article-title: A parallel graph coloring heuristic publication-title: SIAM Journal of Scientific Computing – volume: 15 start-page: 1036 issue: 4 year: 1986 end-page: 1053 article-title: A simple parallel algorithm for the maximal independent set problem publication-title: SIAM Journal on Computing – volume: 20 start-page: 187 issue: 1 year: 1983 end-page: 209 article-title: Estimation of sparse jacobian matrices and graph coloring problems publication-title: SIAM Journal on Numerical Analysis – year: 2000 – volume: 6 start-page: 47 year: 1981 end-page: 57 article-title: Register allocation via coloring publication-title: Computer Languages – year: 1995 – volume: 77 start-page: 313 year: 1975 end-page: 324 article-title: On coloring random graphs publication-title: Mathematical Proceedings of the Cambridge Philosophical Society – volume: 23 start-page: 591 year: 1976 end-page: 599 article-title: An application of graph coloring to printed circuit testing publication-title: IEEE Transactions on Circuits and Systems – volume: 1541 start-page: 332 year: 1998 end-page: 336 – year: 1979 – volume: 35 start-page: 8 issue: 1 year: 1986 end-page: 14 article-title: Some lower bounds for a class of frequency assignment problems publication-title: IEEE Transactions of Vehicular Technology – year: 1992 – year: 1994 – volume: 22 start-page: 251 issue: 4 year: 1979 end-page: 256 article-title: New methods to color the vertices of a graph publication-title: Communications of the ACM – volume: 37 start-page: 171 year: 1996 ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB15 publication-title: Journal of Parallel and Distributed Computing doi: 10.1006/jpdc.1996.0117 – volume: 10 start-page: 85 year: 1967 ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB11 publication-title: Computer Journal doi: 10.1093/comjnl/10.1.85 – year: 1992 ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB16 – volume: 15 start-page: 1036 year: 1986 ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB14 publication-title: SIAM Journal on Computing doi: 10.1137/0215074 – volume: 35 start-page: 8 year: 1986 ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB2 publication-title: IEEE Transactions of Vehicular Technology doi: 10.1109/T-VT.1986.24063 – volume: 23 start-page: 591 year: 1976 ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB4 publication-title: IEEE Transactions on Circuits and Systems doi: 10.1109/TCS.1976.1084138 – volume: 14 start-page: 654 year: 1993 ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB9 publication-title: SIAM Journal of Scientific Computing doi: 10.1137/0914041 – volume: 77 start-page: 313 year: 1975 ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB13 publication-title: Mathematical Proceedings of the Cambridge Philosophical Society doi: 10.1017/S0305004100051124 – year: 1994 ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB1 – year: 1995 ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB5 – volume: 20 start-page: 187 year: 1983 ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB6 publication-title: SIAM Journal on Numerical Analysis doi: 10.1137/0720013 – volume-title: Computers and Intractability year: 1979 ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB7 – volume: 22 start-page: 251 year: 1979 ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB12 publication-title: Communications of the ACM doi: 10.1145/359094.359101 – year: 2000 ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB17 – ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB10 – volume: 6 start-page: 47 year: 1981 ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB3 publication-title: Computer Languages doi: 10.1016/0096-0551(81)90048-5 – volume: 1541 start-page: 332 year: 1998 ident: 10.1002/1096-9128(200010)12:12<1131::AID-CPE528>3.0.CO;2-2-BIB8 |
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| Title | Scalable parallel graph coloring algorithms |
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