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

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

A general framework for shortest path algorithms

In this paper we present a general framework for shortest path algorithms, including amongst others Dijkstra's algorithm and the A* algorithm. By showing that all algorithms are special cases of one algorithm in which some of the nondeterministic choices are made deterministic, termination and correctness can be proved by proving termination and correctness of the root algorithm. Furthermore, several invariants of the algorithms are derived which improve the insight with respect to the operations of the algorithms

Repairing non-monotone ordinal data sets by changing class labels

__Abstract__ Ordinal data sets often contain a certain amount of non-monotone noise. This paper proposes three algorithms for removing these non-monotonicities by relabeling the noisy instances. The first one is a naive algorithm. The second one is a refinement of this naive algorithm which minimizes the difference between the old and the new label. The third one is optimal in the sense that the number of unchanged instances is maximized. The last algorithm is a refinement of the second. In addition, the runtime complexities are discussed

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

Trends in game tree search

This paper deals with algorithms searching trees generated by two-person, zero-sum games with perfect information. The standard algorithm in this field is alpha-beta. We will discuss this algorithm as well as extensions, like transposition tables, iterative deepening and NegaScout. Special attention is devoted to domain knowledge pertaining to game trees, more specifically to solution trees. The above mentioned algorithms implement depth first search. The alternative is best first search. The best known algorithm in this area is Stockman's SSS*. We treat a variant equivalent to SSS* called SSS-2. These algorithms are provably better than alpha-beta, but it needs a lot of tweaking to show this in practice. A variant of SSS-2, cast in alpha-beta terms, will be discussed which does realize this potential. This algorithm is however still worse than NegaScout. On the other hand, applying a similar idea as the one behind NegaScout to this last SSS version yields the best (sequential) game tree searcher known up till now: MTD(f)

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 appropriate hitherto, uses so-called balanced heuristic estimates. In this paper, we focus on symmetric heuristic estimates. First, we show that bidirectional A* using the symmetric heuristic estimate provides us with a feasible approximation. Next a framework is introduced for solving the shortest path problem exactly. It turns out that both the balanced and the symmetric heuristic estimate are instances of a general bidirectional A* framework. The symmetric instance surpasses the balanced instance in space and time

Another view on the SSS* algorithm

A new version of the SSS* algorithm for searching game trees is presented. This algorithm is built around two recursive procedures. It finds the minimax value of a game tree by first establishing an upper bound to this value and then successively trying in a top down fashion to tighten this bound until the minimax value has been obtained. This approach has several advantages, most notably that the algorithm is more perspicuous. Correctness and several other properties of SSS* can now more easily be proven. As an example we prove Pearl's characterization of the nodes visited by SSS*. Finally the new algorithm is transformed into a practical version, which allows an efficient use of memory

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

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