Ewald Speckenmeyer

Ramsey numbers and an approximation algorithm for the vertex cover problem

SummaryWe show two results. First we derive an upper bound for the special Ramsey numbers rk(q) where rk(q) is the largest number of nodes a graph without odd cycles of length bounded by 2k+1 and without an independent set of size q+1 can have. We prove

On enumerating all minimal solutions of feedback problems

r_k (q) \leqq \frac{k}{{k + {\text{1}}}}q^{\frac{{k + {\text{1}}}}{k}} + \frac{{k + {\text{2}}}}{{k + {\text{1}}}}q

On feedback vertex sets and nonseparating independent sets in cubic graphs

The proof is constructive and yields an algorithm for computing an independent set of that size. Using this algorithm we secondly describe an O(¦V¦·¦E¦) time bounded approximation algorithm for the vertex cover problem, whose worst case ratio is

A Satisfiability Formulation of Problems on Level Graphs

\Delta \leqq {\text{2 - }}\frac{{\text{1}}}{{k + {\text{1}}}}

An algorithm for the class of pure implicational formulas

, for all graphs with at most (2k+3)k(2k+2) nodes (e.g. Δ≦1.8, if ¦V¦≦146000).

On linear CNF formulas

We present a fast parallel SAT-solver on a message based MIMD machine. The input formula is dynamically divided into disjoint subformulas. Small subformulas are solved by a fast sequential SAT-solver running on every processor, which is based on the Davis-Putnam procedure with a special heuristic for variable selection. The algorithm uses optimized data structures to modify Boolean formulas. Additionally efficient workload balancing algorithms are used, to achieve a uniform distribution of workload among the processors. We consider the communication network topologiesd-dimensional processor grid and linear processor array. Tests with up to 256 processors have shown very good efficiency-values (>0.95).