{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T12:04:32Z","timestamp":1763467472926},"reference-count":42,"publisher":"Elsevier BV","issue":"1-3","license":[{"start":{"date-parts":[[1999,1,1]],"date-time":"1999-01-01T00:00:00Z","timestamp":915148800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":5311,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Applied Mathematics"],"published-print":{"date-parts":[[1999,1]]},"DOI":"10.1016\/s0166-218x(98)00083-3","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T12:12:16Z","timestamp":1027599136000},"page":"3-26","source":"Crossref","is-referenced-by-count":122,"title":["Spectral partitioning with multiple eigenvectors"],"prefix":"10.1016","volume":"90","author":[{"given":"Charles J","family":"Alpert","sequence":"first","affiliation":[]},{"given":"Andrew B","family":"Kahng","sequence":"additional","affiliation":[]},{"given":"So-Zen","family":"Yao","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0166-218X(98)00083-3_BIB1","series-title":"Proceedings of the ACM\/IEEE Design Automation Conference","first-page":"652","article-title":"Multi-way partitioning via spacefilling curves and dynamic programming","author":"Alpert","year":"1994"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB2","doi-asserted-by":"crossref","first-page":"1342","DOI":"10.1109\/43.469661","article-title":"Multi-way partitioning via geometric embeddings, orderings, and dynamic programming","volume":"14","author":"Alpert","year":"1995","journal-title":"IEEE Trans. CAD"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB3","series-title":"IEEE International Conference on Computer-Aided Design","first-page":"63","article-title":"A general framework for vertex orderings, with applications to netlist clustering","author":"Alpert","year":"1994"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0167-9260(95)00008-4","article-title":"Recent developments in netlist partitioning: a survey","volume":"19","author":"Alpert","year":"1995","journal-title":"Integration: the VLSI J."},{"key":"10.1016\/S0166-218X(98)00083-3_BIB5","series-title":"Proceedings of the ACM\/IEEE Design Automation Conference","first-page":"195","article-title":"Spectral partitioning: the more eigenvectors the better","author":"Alpert","year":"1995"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB6","series-title":"Proceedings of the IEEE International Symposium on Circuits and Systems","first-page":"1172","article-title":"New heuristics and lower bounds for graph partitioning","author":"Arun","year":"1991"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB7","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1002\/cpe.4330060203","article-title":"A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems","volume":"6","author":"Barnard","year":"1994","journal-title":"Concurrency: Practice and Experience"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB8","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1137\/0603056","article-title":"An algorithm for partitioning the nodes of a graph","volume":"3","author":"Barnes","year":"1982","journal-title":"Siam J. Alg. Disc. Meth."},{"key":"10.1016\/S0166-218X(98)00083-3_BIB9","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1137\/0401030","article-title":"An new heuristic for partitioning the nodes of a graph","volume":"3","author":"Barnes","year":"1988","journal-title":"Siam J. Dicrete Math."},{"key":"10.1016\/S0166-218X(98)00083-3_BIB10","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/0166-218X(84)90111-2","article-title":"The indefinite zero-one quadratic problem","volume":"7","author":"Carter","year":"1984","journal-title":"Discrete Appl. Math."},{"key":"10.1016\/S0166-218X(98)00083-3_BIB11","doi-asserted-by":"crossref","first-page":"1088","DOI":"10.1109\/43.310898","article-title":"Spectral k-way ratio cut partitioning and clustering","author":"Chan","year":"1994","journal-title":"IEEE Trans. CAD"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB12","series-title":"Proceedings of the Fifth Design Automation Workshop","first-page":"16.0","article-title":"Efficient partitioning of components","author":"Charney","year":"1968"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB13","first-page":"35","article-title":"The minimization of certain nondifferentiable sums of eigenvalues of symmetric matrices","volume":"vol. 3","author":"Cullum","year":"1975"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB14","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/0012-365X(93)90151-I","article-title":"The performance of an eigenvalue bound on the max-cut problem in some classes of graphs","volume":"111","author":"Delorme","year":"1991","journal-title":"Discrete Math."},{"key":"10.1016\/S0166-218X(98)00083-3_BIB15","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1007\/BF01585184","article-title":"Laplacian eigenvalues and the maximum cut problem","volume":"62","author":"Delorme","year":"1993","journal-title":"Math. Program."},{"key":"10.1016\/S0166-218X(98)00083-3_BIB16","series-title":"Physical Design Automation of VLSI Systems","first-page":"65","article-title":"Logic partitioning","author":"Donath","year":"1988"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB17","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1147\/rd.175.0420","article-title":"Lower bounds for the partitioning of graphs","volume":"17","author":"Donath","year":"1973","journal-title":"IBM J. Res. Dev."},{"key":"10.1016\/S0166-218X(98)00083-3_BIB18","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/BF01581147","article-title":"A computational study of graph partitioning","volume":"66","author":"Falkner","year":"1994","journal-title":"Math. Programm."},{"key":"10.1016\/S0166-218X(98)00083-3_BIB19","doi-asserted-by":"crossref","first-page":"298","DOI":"10.21136\/CMJ.1973.101168","article-title":"Algebraic connectivity of graphs","volume":"23","author":"Fiedler","year":"1973","journal-title":"Czech. Math. J."},{"key":"10.1016\/S0166-218X(98)00083-3_BIB20","series-title":"Proceedings of the IEEE International Conference on Computer-Aided Design","first-page":"414","article-title":"Circuit placements and cost bounds by eigenvector decomposition","author":"Frankle","year":"1986"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB21","first-page":"1","article-title":"Improved approximation algorithms for max k-cut and max bisection","volume":"920","author":"Frieze","year":"1995"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB22","series-title":"Proceedings of the IEEE International Conference on Computer-Aided Design","first-page":"520","article-title":"Finding clusters in VLSI circuits","author":"Garbers","year":"1990"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB23","doi-asserted-by":"crossref","first-page":"1115","DOI":"10.1145\/227683.227684","article-title":"Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming","volume":"42","author":"Goemans","year":"1995","journal-title":"J. ACM"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB24","series-title":"Proceedings of the ACM\/SIAM Symposium on Discrete Algorithms","first-page":"233","article-title":"On the performance of spectral graph partitioning methods","author":"Guattery","year":"1995"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB25","series-title":"Proceedings of the IEEE International Conference on Computer-Aided Design","first-page":"422","article-title":"A new approach to effective circuit clustering","author":"Hagen","year":"1992"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB26","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1109\/43.159993","article-title":"New spectral methods for ratio cut partitioning and clustering","volume":"11","author":"Hagen","year":"1992","journal-title":"IEEE Trans. CAD"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB27","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1109\/43.144852","article-title":"An efficient eigenvector approach for finding netlist partitions","volume":"11","author":"Hadley","year":"1992","journal-title":"IEEE Trans. CAD"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB28","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1287\/mnsc.17.3.219","article-title":"An r-dimensional quadratic placement algorithm","volume":"17","author":"Hall","year":"1970","journal-title":"Mngnt. Sci."},{"key":"10.1016\/S0166-218X(98)00083-3_BIB29","first-page":"28","article-title":"A study of placement techniques","volume":"2","author":"Hanan","year":"1978","journal-title":"J. Des. Automat and Fault-Tolerant Comput."},{"key":"10.1016\/S0166-218X(98)00083-3_BIB30","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1137\/0916028","article-title":"An improved spectral graph partitioning algorithm for mapping parallel computations","volume":"16","author":"Hendrickson","year":"1995","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/S0166-218X(98)00083-3_BIB31","series-title":"VLSI Circuit Layout: Theory and Design","first-page":"87","article-title":"Multiterminal flows in a hypergraph","author":"Hu","year":"1985"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB32","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0020-0190(93)90115-P","article-title":"Modeling hypergraphs by graphs with the same mincut properties","volume":"45","author":"Ihler","year":"1993","journal-title":"Inform. Process. Lett."},{"key":"10.1016\/S0166-218X(98)00083-3_BIB33","series-title":"Combinatorial algorithms for integrated circuit layout","author":"Lengauer","year":"1990"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB34","series-title":"Proceedings of the 6th Quadrennial International Conference on the Theory and Applications of Graphs","first-page":"871","article-title":"The Laplacian spectrum of graphs","author":"Mohar","year":"1988"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB35","series-title":"Proceedings of the ACM\/IEEE Design Automation Conference","first-page":"324","article-title":"A quadratic metric with a simple solution scheme for initial placement","author":"Pillage","year":"1988"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB36","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/0166-218X(94)00155-7","article-title":"Solving the max-cut problem using eigenvalues","volume":"62","author":"Poljak","year":"1995","journal-title":"Discrete Appl. Math."},{"key":"10.1016\/S0166-218X(98)00083-3_BIB37","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1137\/0611030","article-title":"Partitioning sparse matrices with eigenvectors of graphs","volume":"11","author":"Pothen","year":"1990","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"10.1016\/S0166-218X(98)00083-3_BIB38","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/BF02032130","article-title":"A projection technique for partitioning the nodes of a graph","volume":"58","author":"Rendl","year":"1995","journal-title":"Ann. Oper. Res."},{"key":"10.1016\/S0166-218X(98)00083-3_BIB39","series-title":"Proceedings of the ACM\/IEEE Des Automation Conference","first-page":"646","article-title":"Partitioning very large circuits using analytical placement techniques","author":"Riess","year":"1994"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB40","author":"Scott","year":"1980"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB41","series-title":"Spectral partitioning works: planar graphs and finite element meshes","author":"Spielman","year":"1996"},{"key":"10.1016\/S0166-218X(98)00083-3_BIB42","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1109\/31.76488","article-title":"A unified approach to partitioning and placement","volume":"38","author":"Tsay","year":"1991","journal-title":"IEEE Trans. Circuits Systems"}],"container-title":["Discrete Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0166218X98000833?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0166218X98000833?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2021,5,5]],"date-time":"2021-05-05T14:45:41Z","timestamp":1620225941000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0166218X98000833"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,1]]},"references-count":42,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1999,1]]}},"alternative-id":["S0166218X98000833"],"URL":"https:\/\/doi.org\/10.1016\/s0166-218x(98)00083-3","relation":{},"ISSN":["0166-218X"],"issn-type":[{"value":"0166-218X","type":"print"}],"subject":[],"published":{"date-parts":[[1999,1]]}}}