As I mentioned, it's graph bandwidth (see Garey and Johnson). Here are more refs than you would ever want! The Knuth paper is fun -- it's the most complicated algorithm I've ever seen (I think there are 64 different subcases). @article{Papadimitriou:NP-complete, author = {Christos Papadimitriou}, title = {The {NP}-completeness of the Bandwidth Minimization Problem}, journal = {Computing}, volume = 16, pages = {263--270}, year = 1976} @article{Garey:bandwidth, author = {Michael Garey and Ronald Graham and David Johnson and Donald Knuth}, title = {Complexity Results for Bandwidth Minimization}, journal = SIAMJAM, volume = 34, pages = {477--495}, year = 1978} @incollection{Cuthill:strategies, author = {Elizabeth Cuthill}, title = {Several Strategies for Reducing the Bandwidth of Matrices}, booktitle = {Sparse Matrices and Their Applications}, editor = {D. J. Rose and R. A. Willoughby}, publisher = {Plenum Press, New York}, year = 1972} @article{Gibbs:algorithm, author = {Norman Gibbs and William Poole and Paul Stockmeyer}, title = {An Algorithm for Reducing the Bandwidth and Profile of a Sparse Matrix}, journal = {{SIAM} Journal of Numerical Analysis}, volume = 13, number = 2, month = {April}, year = 1976} @Article{Chinn:survey, author = "P. Z. Zinn and J. Chv\'atalov\'a and A. K. Dewdney and N. E. Gibbs", title = "The Bandwidth Problem for Graphs and Matrices --- A Survey", journal = "Journal of Graph Theory", year = "1982", volume = "6", number = "3", pages = "223--254" } @Article{Saxe:dynamic, author = "James Saxe", title = "Dynamic Programming Algorithms for Recognizing Small Bandwidth Graphs in Polynomial Time", journal = SIAMJADM, year = "1980", volume = "1", number = "4", pages = "363--369", month = dec } @Article{Gurari:improved, author = "Eitan Gurari and Ivan Sudborough", title = "Improved Dynamic Programming Algorithms for Bandwidth Minimization and the MinCut Linear Arrangement Problem", journal = JALG, year = "1984", volume = "5", OPTnumber = "4", pages = "531--546", month = dec } @Article{Monien:TCS, author = "Burkhard Monien and Ivan Sudborough", title = "Bandwidth Constrained {NP}-Complete Problems", journal = TCS, year = "1985", volume = "41", pages = "141--167" }