Sequential and Parallel Algorithms for Mixed Packing and Covering
Abstract
Mixed packing and covering problems are problems that can be formulated as linear programs using only nonnegative coefficients. Examples include multicommodity network flow, the HeldKarp lower bound on TSP, fractional relaxations of set cover, binpacking, knapsack, scheduling problems, minimumweight triangulation, etc. This paper gives approximation algorithms for the general class of problems. The sequential algorithm is a simple greedy algorithm that can be implemented to find an epsilonapproximate solution in O(epsilon^2 log m) lineartime iterations. The parallel algorithm does comparable work but finishes in polylogarithmic time. The results generalize previous work on pure packing and covering (the special case when the constraints are all "lessthan" or all "greaterthan") by Michael Luby and Noam Nisan (1993) and Naveen Garg and Jochen Konemann (1998).
 Publication:

arXiv eprints
 Pub Date:
 May 2002
 arXiv:
 arXiv:cs/0205039
 Bibcode:
 2002cs........5039Y
 Keywords:

 Computer Science  Data Structures and Algorithms;
 F.2.1;
 G.1.6
 EPrint:
 doi:10.1109/SFCS.2001.959930