Stephen Suen

Analysis of Two Simple Heuristics on a Random Instance ofk-sat

We consider the performance of two algorithms, GUC and SC studied by M. T. Chao and J. Franco SIAM J. Comput.15(1986), 1106?1118;Inform. Sci.51(1990), 289?314 and V. Chvatal and B. Reed in“Proceedings of the 33rd IEEE Symposium on Foundations of Computer Science, 1992,” pp. 620?627, when applied to a random instance ? of a boolean formula in conjunctive normal form withnvariables and ?cn? clauses of sizekeach. For the case wherek=3, we obtain the exact limiting probability that GUC succeeds. We also consider the situation when GUC is allowed to have limited backtracking, and we improve an existing threshold forcbelow which almost all ? is satisfiable. Fork?4, we obtain a similar result regarding SC with limited backtracking.

The Probability of Unique Solutions of Sequencing by Hybridization

We determine the asymptotic limiting probability as m-->infinity that a random string of length m over some alphabet sigma can be determined uniquely by its substrings of length l. This is an abstraction of a problem faced when trying to sequence DNA clones by SBH.

Optimal Construction of Edge-Disjoint Paths in Random Graphs

Given a graph G=(V,E) with n vertices, m edges, and a family of

Randomized greedy matching. II

\kappa

On the independence number of random cubic graphs

pairs of vertices in

Counting the Number of Hamilton Cycles in Random Digraphs

V

Analysis of a Simple Greedy Matching Algorithm on Random Cubic Graphs

, we are interested in finding for each pair (ai, bi) a path connecting ai to bi such that the set of

Some Results for the Acceptance Urn Model

\kappa

An Improbable Game of Darts

paths so found is edge disjoint. (For arbitrary graphs the problem is

Inequality Related to Vizing's Conjecture

{\cal NP}