Showing papers by "Richard Cole published in 1997"

Tree pattern matching and subset matching in randomized O(nlog3m) time

Abstract: lle main goal of this paper is to give an efficient algorithm for the Tree Pattern Matching problem. We also introduce and give an efficient algorithm for the Subset Matching problem. The Subset Matching problem is to find all occurrences of a pattern string p of length m in a text string t of length n, where each pattern and text location is a set of characters drawn from some alphabet. The pattern is said to occur at text position i if the set p~] is a subset of the set t[i + j – 1], for allj, 1< j < m. Wegivean O((s+ n)log2 mlog(s + n)) randomized algorithm for this problem, wheres denotes the sum of the sizes of all the sets. Then we reduce the Tree Pattern Matching problem to a number of instances of the Subset Matching problem. This reduction takes linear time and the sum of the sizes of the Subset Matching problems obtained is also linear. Coupled with our first result, this implies an O(n logz m log n) time randomized algorithm for the Tree Pattern Matching problem.

Reconfiguring Arrays with Faults Part I: Worst-Case Faults

Abstract: In this paper we study the ability of array-based networks to tolerate worst-case faults. We show that an $N \times N$ two-dimensional array can sustain $N^{1-\epsilon}$ worst-case faults, for any fixed $\epsilon > 0$, and still emulate $T$ steps of a fully functioning $N \times N$ array in $O(T+N)$ steps, i.e., with only constant slowdown. Previously, it was known only that an array could tolerate a constant number of faults with constant slowdown. We also show that if faulty nodes are allowed to communicate, but not compute, then an $N$-node one-dimensional array can tolerate $\log^k N$ worst-case faults, for any constant $k > 0$, and still emulate a fault-free array with constant slowdown, and this bound is tight.