Heuristic estimates in shortest path algorithms

Shortest path problems occupy an important position in Operations Research aswell as in Arti¯cial Intelligence. In this paper we study shortest path algorithms thatexploit heuristic estimates. The well-known algorithms are put into one framework.Besides we present an interesting application of binary numbers in the shortest paththeory.operations research;graph theory;network flows;search problems

Dilworth's Theorem Revisited, an Algorithmic Proof

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.

Yet another bidirectional algorithm for shortest paths

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 processes of the two sides do not meet, we are in the main phase. %As soon as a meeting point is obtained, the post-phase is in progress. \\\\ The version of bidirectional~A* that is considered the most appropriate in literature hitherto, uses so-called balanced heuristic estimates. This means that the two estimates of the two directions are in balance, i.e., their sum is a constant value. In this paper, we do not restrict ourselves any longer to balanced heuristics. A generalized version of bidirectional A* is proposed, where the heuristic estimate does not need to be balanced. This new version turns out to be faster than the one with the balanced heuristic.shortest path;bidirectional search;road network search

A new bidirectional algorithm for shortest paths

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 so-called balanced heuristic estimates.This means that the two estimates of the two directions are in balance, i.e., their sum is a constant value.In this paper, we do not restrict ourselves any longer to balanced heuristics.A generalized version of bidirectional A* is proposed, where the heuristic estimate does not need to be balanced.This new version turns out to be faster than the one with the balanced heuristic.shortest path;bidirectional search;road network search

Mining frequent itemsets a perspective from operations research

Many papers on frequent itemsets have been published. Besides somecontests in this field were held. In the majority of the papers the focus ison speed. Ad hoc algorithms and datastructures were introduced. Inthis paper we put most of the algorithms in one framework, usingclassical Operations Research paradigms such as backtracking, depth-first andbreadth-first search, and branch-and-bound. Moreover we presentexperimental results where the different algorithms are implementedunder similar designs.data mining;operation research;Frequent itemsets

Classification and Target Group Selection Based Upon Frequent Patterns

In this technical report , two new algorithms based upon frequent patterns are proposed. One algorithm is a classification method. The other one is an algorithm for target group selection. In both algorithms, first of all, the collection of frequent patterns in the training set is constructed. Choosing an appropriate data structure allows us to keep the full collection of frequent patterns in memory. The classification method utilizes directly this collection. Target group selection is a known problem in direct marketing. Our selection algorithm is based upon the collection of frequent patterns.classification;association rules;frequent item sets;target group selection

Unifying LL and LR parsing

In parsing theory, LL parsing and LR parsing are regarded to be two distinct methods. In this paper the relation between these methods is clarified.As shown in literature on parsing theory, for every context-free grammar, a so-called non-deterministic LR(0) automaton can be constructed. Here, we show, that traversing this automaton in a special way is equivalent to LL(1) parsing. This automaton can be transformed into a deterministic LR-automaton. The description of a method to traverse this automaton results into a new formulation of the LR parsing algorithm. Having obtained in this way a relationship between LL and LR parsing, the LL(1) class is characterised, using several LR-classes

How to find frequent patterns?

An improved version of DF, the depth-first implementation of Apriori, is presented.Given a database of (e.g., supermarket) transactions, the DF algorithm builds a so-called trie that contains all frequent itemsets, i.e., all itemsets that are contained in at least `minsup' transactions with `minsup' a given threshold value.In the trie, there is a one-to-one correspondence between the paths and the frequent itemsets.The new version, called DF+, differs from DF in that its data structure representing the database is borrowed from the FP-growth algorithm. So it combines the compact FP-growth data structure with the efficient trie-building method in DF.

Bidirectional A*: comparing balanced and symmetric heuristic methods

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 appropriatehitherto, uses so-called balanced heuristic estimates. In this paper, we focus on symmetric heuristic estimates. First, we show that bidirectional A* using the symmetricheuristic estimate provides us with a feasible approximation. Next a framework is introduced for solving the shortest path problem exactly. It turns out that both thebalanced and the symmetric heuristic estimate are instances of a general bidirectional A* framework. The symmetric instance surpasses the balanced instance in space andtime.operations research;graph theory;network flow;search;shortest path

The minimum spanning tree and duality in graphs

Several algorithms for the minimum spanning tree are known. The Blue-red algorithm is a generic algorithm in this field. A new proof for this algorithm is presented, based upon the duality of circuits and cuts in a graph. The Blue-red algorithm is genetic, because the other algorithms can be regarded as special instances. This is shown using the same duality