Jiří Fink

Sofia Brenner, Jiří Fink

We present an algorithm that enumerates all ideals of an input poset with constant delay in Gray code order, i.e., such that consecutively visited ideals differ in at most three elements. This answers a long-standing open problem posed by Pruesse and Ruskey, and improves upon previous algorithms by Pruesse and Ruskey, Squire, Habib, Medina, Nourine and Steiner, as well as Abdo. Using the same techniques, we also obtain an algorithm that enumerates all antichains of an input poset with constant delay such that successively visited antichains differ in at most three elements. As a key technical ingredient, we introduce a new potential-based analysis framework for recursive algorithms, which we call the Pyramid method. We show that this method subsumes the Push-out method of Uno. Beyond the present application, the Pyramid method is a general framework to analyze recursive algorithms and may thus be of independent interest.

Stefan Edelkamp, Jiří Fink, Petr Gregor et al.

This paper is based on Bylander's results on the computational complexity of propositional STRIPS planning. He showed that when only ground literals are permitted, determining plan existence is PSPACE-complete even if operators are limited to two preconditions and two postconditions. While NP-hardness is settled, it is unknown whether propositional STRIPS with operators that only have one precondition and one effect is NP-complete. We shed light on the question whether this small solution hypothesis for STRIPS$^1_1$ is true, calling a SAT solver for small instances, introducing the literal graph, and mapping it to Petri nets.

Jiří Fink, Martin Loebl, Petra Pelikánová

This paper studies large scale instances of a fairly general arc-routing problem as well as incorporate practical constraints in particular coming from the scheduling problem of the winter road maintenance (e.g. different priorities for and methods of road maintenance). We develop a new algorithm based on a bin-packing heuristic which is well-scalable and able to solve road networks on thousands of crossroads and road segments in few minutes. Since it is impossible to find an optimal solution for such a large instances to compare it with a result of our algorithm, we also develop techniques to compute lower bounds which are based on Integer Linear Programming and Lazy Constraints.