Young-Soo Myung

On the generalized minimum spanning tree problem

This paper considers the Generalized Minimum Spanning Tree Problem (GMSTP). Given an undirected graph whose nodes are partitioned into mutually exclusive and exhaustive node sets, The GMSTP is then to find a minimum-cost tree which includes exactly one node from each node set. Here, we show that the GMSTP is NP-hard and that unless P = NP no polynomial-time heuristic algorithm with a finite worst-case performance ratio can exist for the GMSTP. We present various integer programming formulations for the problem and compare their linear programming relaxations. Based on the tightest formulation among the ones proposed, a dual-based solution procedure is developed and shown to be efficient from computing experiments.

Optimal Load Balancing on Sonet Bidirectional Rings

In this paper we consider the Ring Loading Problem, which arises in the design of SONET bidirectional rings. The issue of demand splitting divides the ring loading problem into the two kinds. One allows a demand to be split and routed in two different directions and the other does not. The former kind becomes a relaxation of the latter. We present an efficient exact solution procedure for the case with demand splitting, and a two-approximation algorithm for the case without demand splitting. Computational results are also shown to prove the efficiency of the proposed procedures.

A cutting plane algorithm for computing k-edge survivability of a network

Abstract Given an undirected network and a set of traffic demands between pairs of nodes, k - edge survivability of a given network is defined as the percentage of the total traffic surviving the failure of k edges in the worst case. The problem of computing k -edge survivability is known to be NP-hard and no algorithm other than simple enumeration has been found. In this paper, we develop an efficient algorithm for generating lower and upper bounds of k -edge survivability of a network. We present a preprocessing procedure of reducing the problem size, a heuristic of providing a lower bound, and a cutting plane algorithm of obtaining an upper bound. Computational results for evaluating the performance of the proposed algorithm are also presented.

Optimal design of a distributed network with a two-level hierarchical structure

Abstract This paper deals with the topological design of a network with a two-level hierarchical structure where the embedded backbone network is full-meshed and the local networks attached to it are of star type. The whole problem, unlike the conventional approaches partitioning it into two subproblems, is directly handled in such a general setting that both a backbone network and local access networks are to be simultaneously determined. We formulate this problem as a quadratic 0–1 programming model, and also propose an equivalent linearized version of the model. Based on the observation that the linearized model is a variant of the well established uncapacitated facility location problem, a dual-based solution procedure is developed and shown to be efficient from computing experiments which were done on a wide variety of problems with up to 50 backbone nodes and 50 user nodes.

A bi-objective uncapacitated facility location problem

Abstract We consider a bi-objective model for uncapacitated facility location where one objective is to maximize the net profit and the other to maximize the profitability of the investment. We first characterize the structure of the model having both a linear and a fractional objective function. In order to generate efficient solutions for the model, we develop a heuristic procedure which has computational advantages over existing methods. A numerical example is presented to illustrate the solution process and computational tests on large scale problems are also provided.

Base station location in a cellular CDMA system

We consider a cellular CDMA system in which blocking is enforced when the relative interference exceeds a certain threshold level. This paper addresses a radio network design problem in such a CDMA system. Given the data of call‐traffic distributed over the service area and potential sites of base stations, the objective of the problem is to locate base stations so as to minimize the associated cost for establishing base stations while keeping the probability of blocking under control. We develop an efficient algorithm for solving the design problem. Computational experiments with real‐world data are conducted to show both the efficiency and the practicality of the proposed design method.

A network flow model for the optimal allocation of both foldable and standard containers

This paper considers a multi-port and multi-period container planning problem of shipping companies that use both standard and foldable containers. A company must decide which number of empty containers of each type to purchase and reposition at each port within a defined period to minimize the total purchasing, repositioning, and storage costs.We develop a model to optimally allocate both foldable and standard containers. We show that a single commodity minimum cost network flow algorithm solves the problem by proving that a two commodity flow problem can be modeled as a single commodity flow problem.

Multicommodity flows in cycle graphs

This paper considers the multicommodity flow problem and the integer multicommodity flow problem on cycle graphs. We present two linear time algorithms for solving each of the two problems.

Parametric uncapacitated facility location

We consider the parametric Uncapacitated Facility Location Problem (UFLP) where the demand of each customer is allowed to vary over a certain interval. Despite the value of parametric analysis, no such efforts are found for the UFLP, that mainly seems to be due to the fact that parametric analysis usually requires the computation of a number of UFLPs with heavy computational burden. In this paper, we will show that the special structure of the UFLP provides a nice property for its parametric version, based on which an efficient branch and bound procedure for the parametric analysis is developed.

On the clique partitioning problem in weighted interval graphs

The minimum clique partitioning problem in weighted interval graphs (MCPI) is defined as follows. Given an interval graph with nonnegative node weights, the problem is to partition the nodes into a set of cliques such that the sum of node weights in each clique is no more than a given bound. The objective of the problem is to minimize the number of cliques. Recently, Chen et al. [M. Chen, J. Li, J. Li, W. Li, and L. Wang, Some approximation algorithms for the clique partitioning problem in weighted interval graphs, Theoretical Computer Science 381 (2007), 124-133] proposed three approximation algorithms having constant factors 3, 2.5 and 2, and a linear time optimal algorithm for the case with identical weights. In this paper, we show that their factor 2 algorithm does not achieve the expected approximation ratio and the linear time algorithm cannot give an optimal solution for the identical weights case. We also develop an approximation algorithm with factor 2 for the variable weights case and an exact algorithm for the identical weights case.