A Prolog Technique of Implementing Search of A/O Graphs with Constraints

Our research has been motivated by the task of forming a solution subgraph which satisifies given constraints. The problem is represented by an A/O graph. Our approach is to apply a suitably modified technique of dependency-directed backtracking. We present our formulation of the standard chronological backtracking algorithm in Prolog. Based on it, we have developed an enhanced algorithm which makes use of special heuristic knowledge. It involves also the technique of node marking. We have gathered experience with the prototype Prolog implementation of the algorithm in applying it to (one step of) the problem of building a software configuration. Our experience shows that Prolog programming techniques offer a considerable flexibility in implementing the above outlined tasks

Certification of proving termination of term rewriting by matrix interpretations

Contains fulltext : 71920.pdf (preprint version ) (Open Access)34th Conference on Current Trends in Theory and Practice of Computer Science, Nový Smokovec, Slovakia, January 19-25, 2008., 19 januari 200

Untangling a planar graph

In John Tantalo’s on-line game Planarity the player is given a non-plane straight-line drawing of a planar graph. The aim is to make the drawing plane as quickly as possible by moving vertices. Pach and Tardos have posed a related problem: can any straight-line drawing of any planar graph with n vertices be made plane by vertex moves while keeping vertices fixed for some absolute constant ? It is known that three vertices can always be kept (if n¿=¿5). We still do not solve the problem of Pach and Tardos, but we report some progress. We prove that the number of vertices that can be kept actually grows with the size of the graph. More specifically, we give a lower bound of on this number. By the same technique we show that in the case of outerplanar graphs we can keep a lot more, namely vertices. We also construct a family of outerplanar graphs for which this bound is asymptotically tight