Polynomial Time Algorithms for the Min Cut Problem on Degree Restricted Trees

Polynomial algorithms are described that solve the MIN CUT LINEAR ARRANGEMENT problem on degree restricted trees. For example, the cutwidth or folding number of an arbitrary degree d tree can be found in O(n(logn)d-2) steps. This also yields an algorithm for determining the black/white pebble demand of degree three trees. A forbidden subgraph characterization is given for degree three trees having cutwidth k. This yields an interesting corollary: for degree three trees, cutwidth is identical to search number.

[1]  A. Feller.  Automatic layout of low-cost quick-turnaround random-logic custom LSI devices , 1976, DAC '76.

[2]  Robert E. Tarjan,et al.  The Space Complexity of Pebble Games on Trees , 1980, Inf. Process. Lett..

[3]  Thomas Lengauer.  Upper and Lower Bounds on the Complexity of the Min-Cut Linear Arrangement Problem on Trees , 1982 .

[4]  Friedhelm Meyer auf der Heide,et al.  A Comparison of two Variations of a Pebble Game on Graphs , 1981, Theor. Comput. Sci..

[5]  Christos H. Papadimitriou,et al.  The Complexity of Searching a Graph (Preliminary Version) , 1981, FOCS.

[6]  David S. Johnson,et al.  Some Simplified NP-Complete Graph Problems , 1976, Theor. Comput. Sci..

[7]  Ivan Hal Sudborough,et al.  Bandwidth constrained NP-Complete problems , 1981, STOC '81.

[8]  David S. Johnson,et al.  COMPLEXITY RESULTS FOR BANDWIDTH MINIMIZATION , 1978 .

[9]  F. Makedon.  Layout problems and their complexity , 1982 .

[10]  T. D. Parsons,et al.  Pursuit-evasion in a graph , 1978 .

[11]  Nicholas Pippenger,et al.  Advances in Pebbling (Preliminary Version) , 1982, ICALP.

[12]  Yossi Shiloach,et al.  A Minimum Linear Arrangement Algorithm for Undirected Trees , 1979, SIAM J. Comput..

[13]  室 章治郎.  Michael R.Garey/David S.Johnson 著, "COMPUTERS AND INTRACTABILITY A guide to the Theory of NP-Completeness", FREEMAN, A5判変形判, 338+xii, \5,217, 1979 , 1980 .

[14]  Roman R. Redziejowski.  On arithmetic expressions and trees , 1969, CACM.

[15]  J. Moon.  Counting labelled trees , 1970 .