Clyde L. Monma

Bio: Clyde L. Monma is an academic researcher from Telcordia Technologies. The author has contributed to research in topics: Minimum spanning tree & Network planning and design. The author has an hindex of 25, co-authored 33 publications receiving 2445 citations.

On the Complexity of Scheduling with Batch Setup Times

Abstract: Many practical scheduling problems involve processing several batches of related jobs on common facilities where a setup time is incurred whenever there is a switch from processing a job in one batch to a job in another batch. We extend various scheduling models to include batch setup times. The models include the one-machine maximum lateness, total weighted completion time, and number of late jobs problems. In all these cases, a dynamic programming approach results in an algorithm that is polynomially bounded in the number of jobs, but is exponential in the number of batches. We also study the parallel machine model with preemption and show that the maximum completion time, maximum lateness, total weighted completion time, and number of late jobs problems are NP-hard, even for the case of two identical parallel machines, and sequence independent setup times.

Send-and-split method for minimum-concave-cost network flows

Abstract: Many problems from inventory, production and capacity planning, and from network design, exhibit scale economies and can be formulated in terms of finding minimum-additive-concave-cost nonnegative network flows. We reduce the problem to an equivalent one in which the arc flow costs are nonnegative and give a dynamic-programming method, called the send-and-split method, to solve it. The main work of the method entails repeatedly solving set-splitting and minimum-cost-chain problems. In uncapacitated networks with n nodes, a arcs, and d + 1 demand nodes, i.e., nodes with nonzero exogenous demand, the algorithm requires up to n2-13d + s2d operations additions and comparisons where s = n log2n + 3a is the number of operations required to solve a minimum-cost-chain problem with nonnegative arc costs on the augmented graph formed by appending a node and an arc thereto from each node in the graph. If also the network is k-planar, i.e., the graph is planar with all demand nodes lying on the boundary of k faces, the method requires at most n2-kd3k + sd2k operations. The algorithm can be applied to capacitated networks because they can be reduced to equivalent uncapacitated ones. These results unify, significantly generalize e.g., to cyclic problems, and sometimes improve upon e.g., for tandem facilities known polynomial-time dynamic-programming algorithms for Wagner and Whitin's Wagner, H. M., Whitin, T. M. 1958. Dynamic version of the economic lot size model. Management Sci.5 89--96. dynamic economic-order-quantity problem, Zangwill's Zangwill, W. I. 1969. A backlogging model and a multi-echelon model of a dynamic economic lot size production system---A network approach. Management Sci.15 506--527. generalization to tandem facilities, and Veinott's Veinott, Jr., A. F. 1969. Minimum concave-cost solution of Leontief substitution models of multi-facility inventory systems. Oper. Res.17 262--291. increasing-capacity warehousing problem. The networks for the finite-period versions of these problems are each 1-planar. The method improves upon Zangwill's Zangwill, W. I. 1968. Minimum concave cost flows in certain networks. Management Sci.14 429--450. related Oand running-time dynamic-programming method for finding minimum-additive-concave-cost non-negative flows in circuitless single-source networks. We also implement the method to solve in polynomial time the d + 1-demand-node and k-planar versions of the minimum-cost forest and Steiner problems in graphs. The running time for the d + 1-demand-node Steiner problem in graphs is comparable to that of Dreyfus and Wagner's Dreyfus, S. E., Wagner, R. A. 1971. The Steiner problem in graphs. Networks1 195--207. method.

Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints

Abstract: We describe a cutting plane approach to the problem of designing survivable fiber optic communication networks. This problem can be formulated as a minimum cost network design problem with certain low-connectivity constraints. Computational results on real-world telephone network design problems demonstrate the effectiveness of our cutting plane method. The facet-inducing inequalities for the convex hull of the solutions to this problem on which our algorithm is based are studied in detail in a companion paper.

Methods for Designing Communications Networks with Certain Two-Connected Survivability Constraints

Abstract: In this paper, we consider the problem of designing a minimum cost communication network subject to certain two-connected survivability constraints This problem was motivated by work at Bellcore on planning fiber optic communications networks We introduce heuristics for constructing initial feasible networks, and local improvement heuristics for reducing the cost of existing network designs while preserving a feasible network This approach is shown to be effective on data from both real-world fiber optic communications network problems and randomly generated problems

Transitions in geometric minimum spanning trees

Abstract: We study some combinatorial and algorithmic problems associated with an arbitrary motion of input points in space. The motivation for such an investigation comes from two different sources:computer modeling andsensitivity analysis. In modeling, the dynamics enters the picture since geometric objects often model physical entities whose positions can change over time. In sensitivity analysis, the motion of the input points might represent uncertainties in the precise location of objects. The main results of the paper deal with state transitions in the minimum spanning tree when one or more of the input points move arbitrarily in space. In particular, questions of the following form are addressed: (i) How many different minimum spanning trees can arise if one point moves while the others remain fixed? (ii) When does the minimum spanning tree change its topology if all points are allowed to move arbitrarily?

Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey

Abstract: The theory of deterministic sequencing and scheduling has expanded rapidly during the past years. In this paper we survey the state of the art with respect to optimization and approximation algorithms and interpret these in terms of computational complexity theory. Special cases considered are single machine scheduling, identical, uniform and unrelated parallel machine scheduling, and open shop, flow shop and job shop scheduling. We indicate some problems for future research and include a selective bibliography.

Digraphs Theory Algorithms And Applications

Abstract: The theory of directed graphs has developed enormously over recent decades, yet this book (first published in 2000) remains the only book to cover more than a small fraction of the results. New research in the field has made a second edition a necessity. Substantially revised, reorganised and updated, the book now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems. As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem. Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject. Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science. It will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

Parameterized Algorithms

Abstract: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.