Dilworth's theorem establishes a link between a minimal path cover and a maximal antichain in a digraph. A new proof for Dilworth's theorem is given. Moreover an algorithm to find both the path cover and the antichain, as considered in the theorem, is presented.

We visualize a a web server log by means of multidimensional scaling. To that end, a so-called dissimilarity metric is introduced in the sets of sessions and pages respectively. We interpret the resulting visualizations and find some interesting patterns.

For finding a shortest path in a network the bidirectional A* algorithm is a widely known algorithm. An A* instance requires a heuristic estimate, a real-valued function on the set of nodes. The version of bidirectional~A* that is considered the most appropriate in literature hitherto, uses...

Many papers on frequent itemsets have been published. Besides some contests in this field were held. In the majority of the papers the focus is on speed. Ad hoc algorithms and datastructures were introduced. In this paper we put most of the algorithms in one framework, using classical Operations...

A widely known algorithm for ¯nding the shortest path in a network is Bidirectional A*. The version of bidirectional A* that is considered the most appropriate hitherto, uses so-called balanced heuristic estimates. In this paper, we focus on symmetric heuristic estimates. First, we show that...

Shortest path problems occupy an important position in Operations Research as well as in Arti¯cial Intelligence. In this paper we study shortest path algorithms that exploit heuristic estimates. The well-known algorithms are put into one framework. Besides we present an interesting...

For finding a shortest path in a network the bidirectional~A* algorithm is a widely known algorithm. An A* instance requires a heuristic estimate, a real-valued function on the set of nodes. %This algorithm distinguishes between the main phase and the postprocessing phase. %As long as the search...

This paper examines the roles of futures prices of crude oil, gasoline, ethanol, corn, soybeans and sugar in the energy-grain nexus. It also investigates the own- and cross-market impacts for lagged grain trading volume and open interest in the energy and grain markets. According to the results,...

This paper examines risk transmission and migration among six US measures of credit and market risk during the full period 2004-2011 period and the 2009-2011 recovery subperiod, with a focus on four sectors related to the highly volatile oil price. There are more long-run equilibrium risk...

We consider the service parts end-of-life inventory problem of a capital goods manufacturer in the final phase of its life cycle. The final phase starts as soon as the production of parts terminates and continues until the last service contract expires. Final order quantities are considered a...