C G ] 5 J ul 2 00 5 An O ( n log n )-Time Algorithm for the Restricted Scaffold Assignment

The restriction scaffold assignment problem takes as input two finite point sets S and T (with S containing more points than T ) and establishes a correspondence between points in S and points in T , such that each point in S maps to exactly one point in T and each point in T maps to at least one point in S. An algorithm is presented that finds a minimum-cost solution for this problem in O(n log n) time, provided that the points in S and T are restricted to lie on a line and the cost function delta is the L(1) metric. This algorithm runs in linear time, if S and T are presorted. This improves the previously best-known O(n (2))-time algorithm for this problem.

[1]  Samir Khuller,et al.  Efficient Minimum Cost Matching and Transportation Using the Quadrangle Inequality , 1995, J. Algorithms.

[2]  Richard M. Karp,et al.  The Restriction Scaffold Problem , 2003, J. Comput. Biol..

[3]  David Avis,et al.  A survey of heuristics for the weighted matching problem , 1983, Networks.

[4]  Michael Werman,et al.  Bipartite Graph Matching for Points on a Line or a Circle , 1986, J. Algorithms.

[5]  H. Kuhn The Hungarian method for the assignment problem , 1955 .

[6]  Robert E. Tarjan,et al.  Fibonacci heaps and their uses in improved network optimization algorithms , 1987, JACM.

[7]  Godfried T. Toussaint,et al.  Classification and Phylogenetic Analysis of African Ternary Rhythm Timelines , 2003 .

[8]  Richard M. Karp,et al.  Two special cases of the assignment problem , 1975, Discrete Mathematics.

[9]  Richard M. Karp,et al.  Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems , 1972, Combinatorial Optimization.

[10]  N. Tomizawa,et al.  On some techniques useful for solution of transportation network problems , 1971, Networks.

[11]  Alexander Schrijver Min-max Relations for Directed Graphs , 1982 .

[12]  Godfried T. Toussaint,et al.  A Comparison of Rhythmic Similarity Measures , 2004, ISMIR.

[13]  Samuel R. Buss,et al.  Linear and O(n log n) time minimum-cost matching algorithms for quasi-convex tours , 1994, SODA '94.

[14]  Heikki Mannila,et al.  Distance measures for point sets and their computation , 1997, Acta Informatica.

[15]  Judith Keijsper,et al.  An Efficient Algorithm for Minimum-Weight Bibranching , 1998, J. Comb. Theory, Ser. B.

[16]  Godfried T. Toussaint,et al.  El Compás Flamenco: A Phylogenetic Analysis , 2004 .

[17]  Godfried T. Toussaint,et al.  An algorithm for computing the restriction scaffold assignment problem in computational biology , 2005, Inf. Process. Lett..

[18]  ZVI GALIL,et al.  Efficient algorithms for finding maximum matching in graphs , 1986, CSUR.