On the complexity of the one-terminal network design problem

The one-terminal network design problem considered here is to select a subset of the set of potential edges so as to minimize the sum of construction cost plus expected usage cost with discounting. We distinguish between easy and hard cases of this problem.     

The multi-layered network design problem

We address the problem of designing a network built on several layers. This problem occurs in practical applications but has not been studied extensively from the point of view of global optimisation, since the problem of designing a single-layered network is complex. An example of an application is the design of a virtual network (Internet Protocol) built on a sparse optical transport network.     

Minimum concave-cost network flow problems: Applications,complexity, and algorithms

We discuss a wide range of results for minimum concave-cost network flow problems, including related applications, complexity issues, and solution techniques. Applications from production and inventory planning, and transportation and communication network design are discussed. New complexity results are proved which show that this problem is NP-hard for cases with cost functions other than fixed charge. An overview of solution techniques for this problem is presented, with some new results given regarding the implementation of a particular branch-and-bound approach.     

The counting complexity of a simple scheduling problem

Let T be a set of tasks. Each task has a non-negative processing time and a deadline. The problem of determining whether or not there is a schedule of the tasks in T such that a single machine can finish processing each of them before its deadline is polynomially solvable. We prove that counting the number of schedules satisfying this condition is #P-complete.     

Parameterized complexity of spare capacity allocation and the multicost Steiner subgraph problem

We study the computational complexity of the Spare Capacity Allocation problem arising in optical networks that use a shared mesh restoration scheme. In this problem we are given a network with edge capacities and point-to-point demands, and the goal is to allocate two edge-disjoint paths for each demand (a working path and a so-called restoration path, which is activated only if the working path fails) so that the capacity constraints are satisfied and the total cost of the used and reserved bandwidth is minimized. We focus on the setting where we deal with a group of demands together, and select their restoration paths simultaneously in order to minimize the total cost. We investigate how the computational complexity of this problem is affected by certain parameters, such as the number of restoration paths to be selected, or the treewidth of the network graph. To analyze the complexity of the problem, we introduce a generalization of the Steiner Forest problem that we call Multicost Steiner Subgraph. We study its parameterized complexity, and identify computationally easy and hard cases by providing hardness proofs as well as efficient (fixed-parameter tractable) algorithms.     

The parameterized complexity of the induced matching problem

Given a graph G and an integer k≥0, the NP-complete Induced Matching problem asks whether there exists an edge subset M of size at least k such that M is a matching and no two edges of M are joined by an edge of G. The complexity of this problem on general graphs, as well as on many restricted graph classes has been studied intensively. However, other than the fact that the problem is W[1]-hard on general graphs, little is known about the parameterized complexity of the problem in restricted graph classes. In this work, we provide first-time fixed-parameter tractability results for planar graphs, bounded-degree graphs, graphs with girth at least six, bipartite graphs, line graphs, and graphs of bounded treewidth. In particular, we give a linear-size problem kernel for planar graphs.     

An improved Benders decomposition applied to a multi-layer network design problem

Benders decomposition has been widely used for solving network design problems. In this paper, we use a branch-and-cut algorithm to improve the separation procedure of Gabrel et al. and Knippel et al. for capacitated network design. We detail experiments on bi-layer networks, comparing with Knippel’s previous results.     

The complexity of the majority rule on planar graphs

We study the complexity of the majority rule on planar automata networks. We reduce a special case of the Monotone Circuit Value Problem to the prediction problem of determining if a vertex of a planar graph will change its state when the network is updated with the majority rule.     

On the solution and complexity of a generalized linear complementarity problem

We introduce some sufficient conditions under which a generalized linear complementarity problem (GLCP) can be solved as a pure linear complementarity problem. We also establish that the GLCP is in general a NP-Hard problem.Support of this work has been provided by the Instituto Nacional de Investigação Cientifica de Portugal (INIC) under contract 89/EXA/5.     

An extension to rapid transit network design problem

The rapid transit network design problem consists of the location of train alignments and stations, in a context where the demand makes its own decisions about the mode and route. The originality of this study is to incorporate in the model the line locations constraints with a bounded but variable number of lines, and lines with no predetermined origins and destinations. The computational experiments show the necessity of this extension to solve large networks, principally because of its computational advantage. The project has been supported by Ministerio de Educación y Ciencia (Spain) under project TRA-2005-09068-C03-01/MODAL, and by Ministerio de Fomento (Spain) under project 2005/70029/T05.     

A branch-and-price approach to the feeder network design problem

In this paper we consider the problem of designing a container liner shipping feeder network. The designer has to choose which port to serve during many rotations that start and end at a central hub. Many operational characteristics are considered, such as variable leg-by-leg speeds and cargo transit times. Realistic instances are generated from the LinerLib benchmark suite. The problem is solved with a branch-and-price algorithm, which can solve most instances to optimality within one hour. The results also provide insights on the cost structure and desirable features of optimal routes. These insights were obtained by means of an analysis where scenarios are generated varying internal and external conditions, such as fuel costs and port demands.     

Classes of network connectivity and dynamics

Many kinds of complex systems exhibit characteristic patterns of temporal correlations that emerge as the result of functional interactions within a structured network. One such complex system is the brain, composed of numerous neuronal units linked by synaptic connections. The activity of these neuronal units gives rise to dynamic states that are characterized by specific patterns of neuronal activation and co‐activation. These patterns, called functional connectivity, are possible neural correlates of perceptual and cognitive processes. Which functional connectivity patterns arise depends on the anatomical structure of the underlying network, which in turn is modified by a broad range of activity‐dependent processes. Given this intricate relationship between structure and function, the question of how patterns of anatomical connectivity constrain or determine dynamical patterns is of considerable theoretical importance. The present study develops computational tools to analyze networks in terms of their structure and dynamics. We identify different classes of network, including networks that are characterized by high complexity. These highly complex networks have distinct structural characteristics such as clustered connectivity and short wiring length similar to those of large‐scale networks of the cerebral cortex. © 2002 Wiley Periodicals, Inc.     

The computational complexity of basic decision problems in 3-dimensional topology

We study the computational complexity of basic decision problems of 3-dimensional topology, such as to determine whether a triangulated 3-manifold is irreducible, prime, ∂-irreducible, or homeomorphic to a given 3-manifold M. For example, we prove that the problem to recognize whether a triangulated 3-manifold is homeomorphic to a 3-sphere, or to a 2-sphere bundle over a circle, or to a real projective 3-space, or to a handlebody of genus g, is decidable in nondeterministic polynomial time (NP) of size of the triangulation. We also show that the problem to determine whether a triangulated orientable 3-manifold is irreducible (or prime) is in PSPACE and whether it is ∂-irreducible is in coNP. The proofs improve and extend arguments of prior author’s article on the recognition problem for the 3-sphere.      

Use of dynamic trees in a network simplex algorithm for the maximum flow problem

Goldfarb and Hao (1990) have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on ann-vertex,m-arc network in at mostnm pivots and O(n ² m) time. In this paper we describe how to extend the dynamic tree data structure of Sleator and Tarjan (1983, 1985) to reduce the running time of this algorithm to O(nm logn). This bound is less than a logarithmic factor larger than those of the fastest known algorithms for the problem. Our extension of dynamic trees is interesting in its own right and may well have additional applications.Research partially supported by a Presidential Young Investigator Award from the National Science Foundation, Grant No. CCR-8858097, an IBM Faculty Development Award, and AT&T Bell Laboratories.Research partially supported by the Office of Naval Research, Contract No. N00014-87-K-0467.Research partially supported by the National Science Foundation, Grant No. DCR-8605961, and the Office of Naval Research, Contract No. N00014-87-K-0467.     

Algorithms for the non-bifurcated network design problem

In this paper we consider the non-bifurcated network design problem where a given set of cities must be connected by installing on a given set of links integer multiples of some base capacity so that a set of commodity demands can be routed. Each commodity flow is constrained to run through a single path along the network. The objective is to minimize the sum of capacity installation and routing costs. We present an exact algorithm and four new heuristics. The first heuristic generates an initial feasible solution, then it improves it until a necessary condition for optimality is satisfied. Two heuristics are partial enumeration methods and the last one iteratively applies a tabu search method to different initial feasible solutions. Computational results over a set of test problems from the literature show the effectiveness of the proposed algorithms.     

Reliable design of a logistics network under uncertainty: A fuzzy possibilistic-queuing model

This paper proposes a bi-objective model for designing a reliable network of bi-directional facilities in logistics network under uncertainties. For this purpose, the model utilizes an effective reliability approach to find a robust logistics network design. The objectives of the model are to minimize the total costs and the expected transportation costs after failures of bi-directional facilities of the logistics network. To solve the model, a new solution approach is proposed by combining queuing theory, fuzzy possibilistic programming and fuzzy multi-objective programming. Finally, the computational experiments are provided to illustrate the effectiveness of the proposed model and solution approach.     

On the complexity of the car sequencing problem

In this note we give an easier proof of the known result that the car sequencing problem is NP-hard, and point out that it is NP-hard in the strong sense. We show that a previous claim of NP-completeness is incorrect, and instead we give a sufficient condition of membership of NP. We also provide a pseudo-polynomial algorithm for a special case.     

ON THE COMPUTATIONAL COMPLEXITY OF THE MAXIMUM TRADE PROBLEM

ＯＮＴＨＥＣＯＭＰＵＴＡＴＩＯＮＡＬＣＯＭＰＬＥＸＩＴＹＯＦＴＨＥＭＡＸＩＭＵＭＴＲＡＤＥＰＲＯＢＬＥＭＺ．－Ｑ．Ｌｕｏ；Ｄ．Ｌ．ＰＡＲＮＡＳ（ＣｏｍｍｕｎｉｃａｔｉｏｎｓＲｅｓｅａｒｃｈＬａｂｏｒａｔｏｃｙＤｅｐａｒｔｍｅｎｔｏｆＥｌｅｃｔｒｉｃａ...