Markov-Chain-Based Heuristics for the Minimum Feedback Vertex Set Problem

Let G be a directed graph. A vertex set F is called feedback vertex set (FVS) if its removal from G results in an acyclic graph. Because determining a minimum cardinality FVS is known to be NP hard, [Karp72], one is interested in designing fast approximation algorithms determining near-optimum FVSs. The paper presents deterministic and randomised heuristics based on Markov chains. In this regard, an earlier approximation algorithm developed in [Speckenmeyer89] is revisited and refined. Experimental results demonstrate the overall performance superiority of our algorithms compared to other algorithms known from literature with respect to both criteria, the sizes of solutions determined, as well as the consumed runtimes

Clause set structures and satisfiability

We propose a new perspective on propositional clause sets and on that basis we investigate (new) polynomial time SAT-testable classes. Moreover, we study autarkies using a closure concept. A specific simple type of closures the free closures leads to a further formula class called hyperjoins that is studied w.r.t. SAT

Optimal Oblivious Permutation Routing in Small Hypercubes

For each d <= 8 we provide an oblivious algorithm for routing any permutation on the d-dimensional hypercube in at most d communication steps. To prove our result we show that any 1-to-2 d' -routing problem and any 2 d' -to-1-routing problem can be solved in at most d' (d' <= 4) communication steps on a d'-dimensional hypercube. Furthermore we present a class of efficiently working routing algorithms which allows us to make an improved statement about the complexity of some of the provided algorithms

Algorithms for Variable-Weighted 2-SAT and Dual Problems

In this paper we study NP-hard weighted satisfiability optimization problems for the class 2-CNF providing worst-case upper time bounds. Moreover we consider the monotone dual class consisting of clause sets where all variables occur at most twice. We show that weighted SAT, XSAT and NAESAT optimization problems for this class are polynomial time solvable using appropriate reductions to specific polynomial time solvable graph problems

Clause Set Structures and Polynomial-Time SAT-Decidable Classes

Proposing a fibre view on propositional clause sets, we investigate satisfiability testing for several CNF subclasses. Specifically, we show how to decide SAT in polynomial time for formulas where each pair of different clauses intersect either in all or in one variable

Algorithms for Variable-Weighted 2-SAT and Dual Problems

In this paper we study NP-hard weighted satisfiability optimization problems for the class 2-CNF providing worst-case upper time bounds. Moreover we consider the monotone dual class consisting of clause sets where all variables occur at most twice. We show that weighted SAT, XSAT and NAESAT optimization problems for this class are polynomial time solvable using appropriate reductions to specific polynomial time solvable graph problems

Applicability of rescheduling strategies in tram networks

Highly utilized tram networks, where multiple lines share tracks and stations, are inevitably affected by dis-turbances during daily operation. While consequences of small, local perturbations may be counteracted by schedule characteristics, e.g. robustness, long lasting disturbances have to be addressed by dispatchers via schedule adjustments. Several methods for the identification and assessment of different rescheduling actions have been proposed. However, most of these methods have only been applied in railway networks. Therefore, in this paper we compare different rescheduling strategies and assess their applicability in tram networks. This paper begins with a description of possible rescheduling actions and the requirements and limitations to rescheduling strategies in tram networks. Different strategies for railway networks are then described and compared in regard to their applicability in tram networks

A robust schedule for Montpellier's Tramway network

The city of Montpellier in the Languedoc-Roussillon region of France features a fast growing tram network as a central part of its public service infrastructure. Here, as in many other tram networks, resources like tracks and stations are shared between different lines. Because of the resulting dependencies, small inevitable delays can spread through the network and affect its global performance. Abstract This article examines whether a robust tram schedule may help to raise punctuality in Montpellier's tram network. To accomplish this, we apply a tool set designed to generate schedules optimized for robustness, which also satisfy given sets of planning requirements. These tools allow to compare time tables with respect to their punctuality and other key indicators. Abstract After an introduction to the goals of this paper, we continue with a description of the tool set focusing on optimization and simulation modules. These software utilities are then employed to generate and simulate robust and non-robust schedules for Montpellier's tram network, which are subsequently compared for the resulting delays

Reducing blocking effects in multi-block layouts

Tour planning in multi-block layouts is a common exercise in logistics. In those systems, blocking effects result from conflicting agents competing for resources. Although clearly exceptional in real world applications, most methods of tour planning assume only one active agent, and thus do not consider blocking effects. In this paper we examine heuristic methods of tour planning in multi-block layouts with multiple agents, finding that blocking effects have a significant impact on system performance. We show that methods devised for the mentioned special case do not scale very well when applied to scenarios with multiple agents. We propose a heuristic method which is capable of reducing blocking effects. It generates tours of equal or shorter length than those produced by the other examined methods

Improving a fixed parameter tractability time bound for the shadow problem

AbstractConsider a forest of k trees and n nodes together with a (partial) function σ mapping leaves of the trees to non-root nodes of other trees. Define the shadow of a leaf ℓ to be the subtree rooted at σ(ℓ). The shadow problem asks whether there is a set S of leaves exactly one from each tree such that none of these leaves lies in the shadow of another leaf in S. This graph theoretical problem as shown in Franco et al. (Discrete Appl. Math. 96 (1999) 89) is equivalent to the falsifiability problem for pure implicational Boolean formulas over n variables with k occurences of the constant false as introduced in: Heusch J. Wiedermann, P. Hajek (Eds.), Proceedings of the Twentieth International Symposium on Mathematical Foundations of Computer Science (MFCS’95), Prague, Czech Republic, Lecture Notes in Computer Science, Vol. 969, Springer, Berlin, 1995, pp. 221–226, where its NP-completeness is shown for arbitrary values of k and a time bound of O(nk) for fixed k was obtained. In Franco et al. (1999) this bound is improved to O(n2kk) showing the problem's fixed parameter tractability (Congr. Numer. 87 (1992) 161). In this paper the bound O(n33k) is achieved by dynamic programming techniques thus significantly improving the fixed parameter part