Problems

This column will carry problems arising in the design of algorithms for discrete problems.Problems are solicited in all areas of algorithm design that are covered byJournal of Algorithms. Some of the problems that appear here may also appear in the “Open Problems” column inSIGACT News. Problems should be submitted to me at the Department of Computer Science, University of Maryland, College Park, MD 20742 (E-mail: samir@cs.umd.edu), and if chosen, will appear in this column. I hope that there will be enough submissions to run this column twice a year. Problem submissions should be precise and succinct. Proposals for guest columns, focusing on problems in a specific research area, are also welcome.Especially welcome are algorithmic problems arising in areas not previously explored by the theoretical computer science community.I have taken over this column from Professor Peter van Emde Boas and I thank him for his efforts in running the column over the past few years.     

Vector Equilibrium Problems,Minimal Element Problems and Least Element Problems

In this paper we introduce some concepts of feasible sets for vector equilibrium problems and some classes of Z-maps for vectorial bifunctions. Under strict pseudomonotonicity assumptions, we investigate the relationship between minimal element problems of feasible sets and vector equilibrium problems. By using Z-maps, we further study the least element problems of feasible sets for vector equilibrium problems. Finally, we prove a generalized sublattice property of feasible sets for vector equilibrium problems associated with Z-maps. This work was supported by the National Natural Science Foundation of China and the Applied Research Project of Sichuan Province (05JY029-009-1). The authors thank Professor Charalambos D. Aliprantis and the referees for valuable comments and suggestions leading to improvements of this paper.     

Problems

This section contains problems and solutions in the design and analysis of algorithms.Problems are solicited in all areas covered by this journal and will be selected for inclusion on the basis of their originality and ability to illustrate fundamental concepts in algorithmic thinking. The submission of exercises from well-known textbooks is not acceptable. Also inappropriate are problems whose statements are excessively long, or vague; and those which use several ad hoc definitions and/or very complex notation. If actual code is to be part of a problem, then an Algol-like syntax is preferred. Proposers should make their problems as precise and unambiguous as possible. Aim for clarity and succinctness.It is expected that a proposer will supply all information relevant to a problem and justifying its interest. Such information will most often include a solution to the problem, or perhaps some special cases. Other background material, such as references of related literature, is especially important for problems submitted without solutions. Well-known unsolved problems are unacceptable. An asterisk before a problem, or part thereof, indicates that neither the proposer nor the editor supplied a solution.Readers wishing to submit problems and/or solutions should observe the following guidelines: All correspondence must be typewritten and submitted in duplicate.Please address all correspondence concerning this section to Peter van Emde Boas, Departments of Mathematics and Computer Science, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, the Netherlands.A number of problems in the Journal of Algorithms will be cross listed in the Bulletin of the European Association for Theoretical Computer Science (BEATCS), and vice versa. Problems listed below whose source is the above Bulletin will be marked by having the initials EATCS appended to the problem number. Such material is reprinted with permission from the BEATCS.The deadline for solutions to the proposed problems is December 31, 1992.