Discrete Applied Mathematics Research Articles

On some optimization problems on k-trees and partial k-trees : Daniel Granot and Darko Skorin-Kapov Discrete Applied Mathematics Vol. 48, 1994, pp. 129–145

On some optimization problems on k-trees and partial k-trees : Daniel Granot and Darko Skorin-Kapov Discrete Applied Mathematics Vol. 48, 1994, pp. 129–145

Parallel algorithms for least median of squares regression

Recently much effort has been devoted to devising robust regression procedures to which the least median of squares (LMS) regression proposed by Rousseeuw ( Journal of the American Statistical Association 79, 1984) belongs. LMS's breakdown point achieves the highest possible value of 50%. It may not be possible to write down closed form expressions for the estimates of LMS and the computations involved are not trivial. Efforts have been made to look for better performance algorithms. Based on the algorithm of Rousseeuw, Steele and Steiger ( Discrete Applied Mathematics 14, 1986) provided a lemma that characterized the computation as a discrete optimization problem with worst time complexity of O( n 3). Souvaine and Steele ( Journal of the American Statistical Association 82, 1987) developed a sweep-line algorithm with time complexity of O( n 2log n). This paper reports the use of parallel computing techniques to speedup the computation of LMS. The Rousseeuw's algorithm and the T-sweep algorithm, an algorithm based on Tukey's idea, have been successfully parallelized, but parallel sweep-line algorithm and its refinement may not work at all in the sense that its performance is untolerantly low due to severe load imbalancing.

On sparse subgraphs preserving connectivity properties

AbstractFrom a theorem of W. Mader [“Über minimal n‐fach zusammenhängende unendliche Graphen und ein Extremal problem,” Arch. Mat., Vol. 23 (1972), pp. 553–560] it follows that a k‐connected (k‐edge‐connected) graph G = (V,E) always contains a k‐connected (k‐edge‐connected) subgraph G′ = (V,E′) with O(k|V|) edges. T. Nishizeki and S. Poljak “K‐Connectivity and Decomposition of Graphs into Forests,” Discrete Applied Mathematics, submitted) showed how G′ can be constructed as the union of k forests. H. Nagamochi and T. Ibaraki [A Linear Time Algorithm for Finding a Sparse k‐Connected Spanning Subgraph of a k‐Connected Graph, Algorithmica, Vol. 7 (1992), pp. 583–596] constructed such a subgraph Gk in linear time and showed for any pair x,y of nodes that Gk contains k openly disjoint (edge‐disjoint) paths connecting x and y if G contains k openly disjoint (edge‐disjoint) paths connecting x and y (even if G is not k‐connected (k‐edge‐connected)). In this article we provide a much shorter proof of a common generalization of the edge‐ and node‐connectivity versions showing that the subgraph Gk has a certain mixed connectivity property. © 1993 John Wiley & Sons, Inc.

Some applications of algebra to combinatorics

Stanley, R.P., Some applications of algebra to combinatorics, Discrete Applied Mathematics 34 (1991) 241-277.

Communications : in our journals Discrete Mathematics and Discrete Applied Mathematics

Communications : in our journals Discrete Mathematics and Discrete Applied Mathematics

Cultures of the Central Highlands, New Guinea

Cultures of the Central Highlands, New Guinea