Wolfgang W. Bein

Bio: Wolfgang W. Bein is an academic researcher from University of Nevada, Las Vegas. The author has contributed to research in topics: Online algorithm & Competitive analysis. The author has an hindex of 13, co-authored 88 publications receiving 744 citations. Previous affiliations of Wolfgang W. Bein include University of Texas at Dallas & University of New Mexico.

Optimal reduction of two-terminal directed acyclic graphs

Abstract: Algorithms for series-parallel graphs can be extended to arbitrary two-terminal dags if node reductions are used along with series and parallel reductions. A node reduction contracts a vertex with unit in-degree (out-degree) into its sole incoming (outgoing) neighbor. This paper gives an $O(n^{2.5} )$ algorithm for minimizing node reductions, based on vertex cover in a transitive auxiliary graph. Applications include the analysis of PERT networks, dynamic programming approaches to network problems, and network reliability. For NP-hard problems one can obtain algorithms that are exponential only in the minimum number of node reductions rather than the number of vertices. This gives improvements if the underlying graph is nearly series-parallel.

Minimum cost flow algorithms for series-parallel networks

Abstract: It is shown that an acyclic multigraph with a single source and a single sink is series-parallel if and only if for arbitrary linear cost functions and arbitrary capacities the corresponding minimum cost flow problem can be solved by a greedy algorithm. Furthermore, for networks of this type with m edges and n vertices, two O(mn + m log m)-algorithms are presented. One of them is based on the greedy scheme.

A Monge property for the d -dimensional transportation problem

Abstract: In 1963, Hoffman gave necessary and sufficient conditions under which a family of O(mn)-time greedy algorithms solves the classical two-dimensional transportation problem with m sources and n sinks. One member of this family, an algorithm based on the «northwest corner rule», is of particular interest, as its running time is easily reduced to O(m+n). When restricted to this algorithm, Hoffman's result can be expressed as follows: the northwest-corner-rule greedy algorithm solves the two-dimensional transportation problem for all source and supply vectors if and only if the problem's cost array C={c[i,j]} possesses what is known as the (two-dimensional) Monge property, which requires c[i 1 ,j 1 ]+c[i 2 ,j 2 ] ≤ c[i 1 ,j 2 ]+c[i 2 ,j 1 ] for i 1

The 3-server problem in the plane

Abstract: In the k-server problem we wish to minimize, in an online fashion, the movement cost of k servers in response to a sequence of requests (we assume that k ≥ 2). The request issued at each step is specified by a point r in a given metric space M. To serve this request, one of the k servers must move to r. It is known that if M has at least k + 1 points then no online algorithm for the k-server problem in M has competitive ratio smaller than k. The best known upper bound on the competitive ratio in arbitrary metric spaces, by Koutsoupias and Papadimitriou (J. ACM 42 (1995) 971), is 2k - 1. There are only a few special cases for which k-competitive algorithms are known: for k = 2, when M is a tree, or when M has at most k + 2 points. We prove that the Work Function Algorithm is 3-competitive for the 3-server problem in the Manhattan plane. As a corollary, we obtain a 4.243-competitive algorithm for 3 servers in the Euclidean plane. The best previously known competitive ratio for 3 servers in these metric spaces was 5.

Cloud storage and online bin packing

Abstract: We study the problem of allocating memory of servers in a data center based on online requests for storage. Given an online sequence of storage requests and a cost associated with serving the request by allocating space on a certain server one seeks to select the minimum number of servers as to minimize total cost. We use two different algorithms and propose a third algorithm. We show that our proposed algorithm performs better for large number of random requests in terms of the variance in the average number of servers.

Resource-constrained project scheduling: Notation, classification, models, and methods

Abstract: Project scheduling is concerned with single-item or small batch production where scarce resources have to be allocated to dependent activities over time. Applications can be found in diverse industries such as construction engineering, software development, etc. Also, project scheduling is increasingly important for make-to-order companies where the capacities have been cut down in order to meet lean management concepts. Likewise, project scheduling is very attractive for researchers, because the models in this area are rich and, hence, difficult to solve. For instance, the resource-constrained project scheduling problem contains the job shop scheduling problem as a special case. So far, no classification scheme exists which is compatible with what is commonly accepted in machine scheduling. Also, a variety of symbols are used by project scheduling researchers in order to denote one and the same subject. Hence, there is a gap between machine scheduling on the one hand and project scheduling on the other with respect to both, viz. a common notation and a classification scheme. As a matter of fact, in project scheduling, an ever growing number of papers is going to be published and it becomes more and more difficult for the scientific community to keep track of what is really new and relevant. One purpose of our paper is to close this gap. That is, we provide a classification scheme, i.e. a description of the resource environment, the activity characteristics, and the objective function, respectively, which is compatible with machine scheduling and which allows to classify the most important models dealt with so far. Also, we propose a unifying notation. The second purpose of this paper is to review some of the recent developments. More specifically, we review exact and heuristic algorithms for the single-mode and the multi-mode case, for the time–cost tradeoff problem, for problems with minimum and maximum time lags, for problems with other objectives than makespan minimization and, last but not least, for problems with stochastic activity durations.

Serial and parallel resource-constrained project scheduling methods revisited: Theory and computation

Abstract: We consider the so-called parallel and serial scheduling method for the classical resource-constrained project scheduling problem. Theoretical results on the class of schedules generated by each method are provided. Furthermore, an in-depth computational study is undertaken to investigate the relationship of single-pass scheduling and sampling for both methods. It is shown that the performance-ranking of priority rules does not differ for single-pass scheduling and sampling, that sampling improves the performance of single-pass scheduling significantly, and that the parallel method cannot be generally considered as superior.

Resource-constrained project scheduling: a survey of recent developments

Abstract: Resource-constrained project scheduling involves the scheduling of project activities subject to precedence and resource constraints in order to meet the objective(s) in the best possible way. The area covers a wide variety of problem types. The objective of this paper is to provide a survey of what we believe are the important recent developments in the area. Our main focus will be on the recent progress made in and the encouraging computational experience gained with the use of optimal solution procedures for the basic resource-constrained project scheduling problem (RCPSP) and important extensions. We illustrate how the branching rules, dominance and bounding arguments of a new depth- first branch-and-bound procedure can be extended to a rich variety of related problems: the generalized resource-constrained project scheduling problem, the resource-constrained project scheduling problem with generalized precedence relations, the preemptive resource-constrained project scheduling problem, the resource availability cost problem, and the resource-constrained project scheduling problem with various time/resource(cost) trade-offs and discounted cash flows.