A Space--Time Tradeoff for Permutation Problems

Many combinatorial problems--such as the traveling salesman, feedback arcset, cutwidth, and treewidth problem-can be formulated as finding a feasible permutation of n elements. Typically, such problems can be solved by dynamic programming in time and space O (2n ), by divide and conquer in time O (4n ) and polynomial space, or by a combination of the two in time O (4n 2-s ) and space O (2s ) for s = n, n/2, n/4, . . .. Here, we show that one can improve the tradeoff to time O (Tn ) and space O (Sn ) with TS < 4 at any 2 < S < 2. The idea is to find a small family of "thin" partial orders on the n elements such that every linear order is an extension of one member of the family. Our construction is optimal within a natural class of partial order families.

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Mikko Koivisto, Pekka Parviainen
• Keywords: Discrete Algorithms, Feasible Permutation, Partial Order Families, Polynomial Space, SODA 2010