Karsten Weihe

Pareto Shortest Paths is Often Feasible in Practice

We study the problem of finding all Pareto-optimal solutions for the multi-criteria single-source shortest-path problem with nonnegative edge lengths. The standard approaches are generalizations of labelsetting (Dijkstra) and label-correcting algorithms, in which the distance labels are multi-dimensional and more than one distance label is maintained for each node. The crucial parameter for the run time and space consumption is the total number of Pareto optima. In general, this value can be exponentially large in the input size. However, in various practical applications one can observe that the input data has certain characteristics, which may lead to a much smaller number -- small enough to make the problem efficiently tractable from a practical viewpoint. In this paper, we identify certain key characteristics, which occur in various applications. These key characteristics are evaluated on a concrete application scenario (computing the set of best train connections in view of travel time, fare, and number of train changes) and on a simplified randomized model, in which these characteristics occur in a very purist form. In the applied scenario, it will turn out that the number of Pareto optima on each visited node is restricted by a small constant. To counter-check the conjecture that these characteristics are the cause of these uniformly positive results, we will also report negative results from another application, in which these characteristics do not occur.

A LINEAR-TIME ALGORITHM FOR EDGE-DISJOINT PATHS IN PLANAR GRAPHS

In this paper we discuss the problem of finding edge-disjoint paths in a planar, undirected graph such that each path connects two specified vertices on the boundary of the graph. We will focus on the “classical” case where an instance additionally fulfills the so-calledevenness-condition. The fastest algorithm for this problem known from the literature requiresO (n5/3(loglogn)1/3) time, wheren denotes the number of vertices. In this paper now, we introduce a new approach to this problem, which results in anO(n) algorithm. The proof of correctness immediately yields an alternative proof of the Theorem of Okamura and Seymour, which states a necessary and sufficient condition for solvability.

Reuse of algorithms: still a challenge to object-oriented programming

This paper is about reusable, efficient implementations of complex algorithms and their integration into software packages. It seems that this problem is not yetwell understood, and that it is not at all clear how object-oriented and other approaches may contribute to a solution. We analyze the problem and try to reduce it to a few key design goals. Moreover, we discuss various existing approaches in light of these goals, and we briefly report experiences with experimental case studies, in which these goals were rigorously addressed.

The Vertex-Disjoint Menger Problem in Planar Graphs

We consider the problem of finding a maximum collection of vertex-disjoint paths in undirected, planar graphs from a vertex

On the Differences between ``Practical'' and ``Applied''

s

Phase synchronization in railway timetables

to a vertex

Moving policies in cyclic assembly line scheduling

t

Minimum strictly convex quadrangulations of convex polygons

. This problem is usually solved using flow techniques, which lead to

Workload balancing in multi-stage production processes

{\cal O}(nk)

Getting Train Timetables into the Main Storage

and