P-Complete Approximation Problems

For P-complete problems such as traveling salesperson, cycle covers, 0-1 integer programming, multicommodity network flows, quadratic assignment, etc., it is shown that the approximation problem is also P-complete. In contrast with these results, a linear time approximation algorithm for the clustering problem is presented.

[1]  Journal of the Association for Computing Machinery , 1961, Nature.

[2]  Ronald L. Graham,et al.  Bounds on Multiprocessing Timing Anomalies , 1969, SIAM Journal of Applied Mathematics.

[3]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[4]  Lawrence Bodin,et al.  A graph theoretic approach to the grouping of ordering data , 1972, Networks.

[5]  D. E. Knuth,et al.  A terminological proposal , 1974, SIGA.

[6]  David S. Johnson,et al.  Some simplified NP-complete problems , 1974, STOC '74.

[7]  David S. Johnson,et al.  Approximation algorithms for combinatorial problems , 1973, STOC.

[8]  Sartaj Sahni,et al.  Computationally Related Problems , 1974, SIAM J. Comput..

[9]  D. J. Rosenkrantz,et al.  Approximate Algorithms for the Traveling Salesperson Problem , 1974, SWAT.

[10]  Edward G. Coffman,et al.  Scheduling independent tasks to reduce mean finishing time , 1974, CACM.

[11]  Eric Keppel,et al.  Approximating Complex Surfaces by Triangulation of Contour Lines , 1975, IBM J. Res. Dev..

[12]  Oscar H. Ibarra,et al.  Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems , 1975, JACM.

[13]  Joseph A. Lukes Combinatiorial Solution to the Partitioning of General Graphs , 1975, IBM J. Res. Dev..

[14]  Richard M. Soland,et al.  A branch and bound algorithm for the generalized assignment problem , 1975, Math. Program..

[15]  Sartaj Sahni,et al.  Approximate Algorithms for the 0/1 Knapsack Problem , 1975, JACM.

[16]  David S. Johnson,et al.  The Complexity of Near-Optimal Graph Coloring , 1976, J. ACM.

[17]  Sartaj Sahni,et al.  Algorithms for Scheduling Independent Tasks , 1976, J. ACM.

[18]  Ellis Horowitz,et al.  Exact and Approximate Algorithms for Scheduling Nonidentical Processors , 1976, JACM.