No abstract

We study the problem of nding a spanning tree with maximum number of leaves. We present a simple 2-approximation algorithm for the problem, improving on the previous best performance ratio of 3 achieved by algorithms of Ravi and Lu. Our algorithm can be implemented to run in linear time using simple data structures. We also study the variant of the problem in which a given subset of vertices are required to be leaves in the tree. We provide a 5=2-approximation algorithm for this version of the problem.

No abstract

The Flexible Job Shop problem is a generalization of the classical job shop scheduling problem in which for every operation there is a group of machines that can process it. The problem is to assign operations to machines and to order the operations on the machines so that the operations can be processed in the smallest amount of time. This models a wide variety of problems encountered in real manufacturing systems. We present a linear time approximation scheme for the non-preemptive version of the problem when the number m of machines and the maximum number \x of operations per job are fixed. We also study the preemptive version of the problem when m and \x are fixed, and present a linear time approximation scheme for the problem without migration and a (2 + ^-approximation algorithm for the problem with migration. Int. J. Found. Comput. Sci. 2005.16:361-379. Downloaded from www.worldscientific.com by MCMASTER UNIVERSITY on 02/06/15. For personal use only.

No abstract

Abstract. The efficiency of regular expression matching algorithms depends very much on the size of the nondeterministic finite automata (NFA) obtained from regular expressions. Reducing the size of these automata by using equivalences has been shown to reduce significantly the search time. We consider the problem of reducing the size of arbitrary NFAs using equivalences and preorders. For equivalences, we give an algorithm to optimally combine equivalent states for reducing the size of the automata. We also show that the problem of optimally using preorders to reduce the size of an automaton is NP-hard.

No abstract

The strip packing problem is to pack a set of rectangles into a strip of fixed width and minimum length. We present asymptotic polynomial time approximation schemes for this problem without and with 90 o rotations. The additive constant in the approximation ratios of both algorithms is 1, improving on the additive term in the approximation ratios of the algorithm by Kenyon and Rémila (for the problem without rotations) and Jansen and van Stee (for the problem with rotations), both of which have a larger additive constant O(1/ε 2 ), ε > 0.The algorithms were derived from the study of the rectangle packing problem: Given a set R of rectangles with positive profits, the goal is to find and pack a maximum profit subset of R into a unit size square bin [0, 1] × [0, 1]. We present algorithms that for any value > 0 find a subset R ⊆ R of rectangles of total profit at least (1 − )OP T , where OP T is the profit of an optimum solution, and pack them (either without rotations or with 90 o rotations) into the augmented bin [0, 1] × [0, 1 + ].