The Subtour Centre Problem

The subtour centre problem is the problem of finding a closed trail S of bounded length on a connected simple graph G that minimises the maximum distance from S to any vertex ofG. It is a central location problem related to the cycle centre and cycle median problems (Foulds et al., 2004; Labbé et al., 2005) and the covering tour problem (Current and Schilling, 1989). Two related heuristics and an integer linear programme are formulated for it. These are compared numerically using a range of problems derived from tsplib (Reinelt, 1995). The heuristics usually perform substantially better then the integer linear programme and there is some evidence that the simpler heuristics perform better on the less dense graphs that may be more typical of applications

Insertion Heuristics for Central Cycle Problems

A central cycle problem requires a cycle that is reasonably short and keeps a the maximum distance from any node not on the cycle to its nearest node on the cycle reasonably low. The objective may be to minimise maximumdistance or cycle length and the solution may have further constraints. Most classes of central cycle problems are NP-hard. This paper investigates insertion heuristics for central cycle problems, drawing on insertion heuristics for p-centres [7] and travelling salesman tours [21]. It shows that a modified farthest insertion heuristic has reasonable worstcase bounds for a particular class of problem. It then compares the performance of two farthest insertion heuristics against each other and against bounds (where available) obtained by integer programming on a range of problems from TSPLIB [20]. It shows that a simple farthest insertion heuristic is fast, performs well in practice and so is likely to be useful for a general problems or as the basis for more complex heuristics for specific problems

Towards Understanding Reasoning Complexity in Practice

Although the computational complexity of the logic underlying the standard OWL 2 for the Web Ontology Language (OWL) appears discouraging for real applications, several contributions have shown that reasoning with OWL ontologies is feasible in practice. It turns out that reasoning in practice is often far less complex than is suggested by the established theoretical complexity bound, which reflects the worstcase scenario. State-of-the reasoners like FACT++, HERMIT, PELLET and RACER have demonstrated that, even with fairly expressive fragments of OWL 2, acceptable performances can be achieved. However, it is still not well understood why reasoning is feasible in practice and it is rather unclear how to study this problem. In this paper, we suggest first steps that in our opinion could lead to a better understanding of practical complexity. We also provide and discuss some initial empirical results with HERMIT on prominent ontologie