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

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

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

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

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

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

Neural Networks for Target Selection in Direct Marketing

Partly due to a growing interest in direct marketing, it has become an important application field for data mining. Many techniques have been applied to select the targets in commercial applications, such as statistical regression, regression trees, neural computing, fuzzy clustering and association rules. Modeling of charity donations has also recently been considered. The availability of a large number of techniques for analyzing the data may look overwhelming and ultimately unnecessary at first. However, the amount of data used in direct marketing is tremendous. Further, there are different types of data and likely strong nonlinear relations amongst different groups within the data. Therefore, it is unlikely that there will be a single method that can be used under all circumstances. For that reason, it is important to have access to a range of different target selection methods that can be used in a complementary fashion. In this respect, learning systems such as neural networks have the advantage that they can adapt to the nonlinearity in the data to capture the complex relations. This is an important motivation for applying neural networks for target selection. In this report, neural networks are applied to target selection in modeling of charity donations. Various stages of model building are described by using data from a large Dutch charity organization as a case. The results are compared with the results of more traditional methods for target selection such as logistic regression and CHAID.neural networks;data mining;direct mail;direct marketing;target selection

Visualizing clickstream data with multidimensional scaling

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