Survivable Networks, Linear Programming Relaxations and the Parsimonious Property

We consider the survivable network design problem - the problem of designing, at minimum cost, a network with edge-connectivity requirements. As special cases, this problem encompasses the Steiner tree problem, the traveling salesman problem and the k-connected network design problem. We establish a property, referred to as the parsimonious property, of the linear programming (LP) relaxation of a classical formulation for the problem. The parsimonious property has numerous consequences. For example, we derive various structural properties of these LP relaxations, we present some algorithmic improvements and we perform tight worstcase analyses of two heuristics for the survivable network design problem

Doubling or Splitting: Strategies for Modeling and Analyzing Survivable Network Design Problems

Survivability is becoming an increasingly important criterion in network design. This paper studies formulations, heuristic worst-case performance, and linear programming relaxations for two classes of survivable network design problems: the low connectivity Steiner (LCS) problem for graphs containing nodes with connectivity requirement of 0, 1, or 2, and a more general multi-connected network with branches (MNB) that requires connectivities of two or more for certain (critical) nodes and single connectivity for other secondary nodes. We consider both unitary and nonunitary MNB problems that respectively require a connected design or permit multiple components. Using a doubling argument, we first show how to generalize heuristic bounds of the Steiner tree and traveling salesman problems to LCS problems. We then develop a disaggregate formulation for the MNB problem that uses fractional edge selection variables to split the total connectivity requirement across each critical cutset into two separate requirements. This model, which is tighter than the usual cutset formulation, has three special cases: a "secondary-peeling" version that peels off the lowest connectivity level, a "connectivity-dividing" version that divides the connectivity requirements for all the critical cutsets, and a "secondarycompletion" version that attempts to separate the design decisions for the multi-connected network from those for the branches. We examine the tightness of the linear programming relaxations for these extended formulations, and then use them to analyze heuristics for the LCS and MNB problems. Our analysis strengthens some previously known heuristic-to-IP worst-case performance ratios for LCS and MNB problems by showing that the same bounds apply to the heuristic-to-LP ratios using our stronger formulations

A knowledge-based system with learning for computer communication network design

Computer communication network design is well-known as complex and hard. For that reason, the most effective methods used to solve it are heuristic. Weaknesses of these techniques are listed and a new approach based on artificial intelligence for solving this problem is presented. This approach is particularly recommended for large packet switched communication networks, in the sense that it permits a high degree of reliability and offers a very flexible environment dealing with many relevant design parameters such as link cost, link capacity, and message delay

Reducing Power Consumption in Backbone Networks

Abstract—According to several studies, the power consumption of the Internet accounts for up to 10 % of the worldwide energy consumption, and several initiatives are being put into place to reduce the power consumption of the ICT sector in general. To this goal, we propose a novel approach to switch off network nodes and links while still guaranteeing full connectivity and maximum link utilization. After showing that the problem falls in the class of capacitated multi-commodity flow problems, and therefore it is NP-complete, we propose some heuristic algorithms to solve it. Simulation results in a realistic scenario show that it is possible to reduce the number of links and nodes currently used by up to 30 % and 50 % respectively during off-peak hours, while offering the same service quality

Spatial optimization for land use allocation: accounting for sustainability concerns

Land-use allocation has long been an important area of research in regional science. Land-use patterns are fundamental to the functions of the biosphere, creating interactions that have substantial impacts on the environment. The spatial arrangement of land uses therefore has implications for activity and travel within a region. Balancing development, economic growth, social interaction, and the protection of the natural environment is at the heart of long-term sustainability. Since land-use patterns are spatially explicit in nature, planning and management necessarily must integrate geographical information system and spatial optimization in meaningful ways if efficiency goals and objectives are to be achieved. This article reviews spatial optimization approaches that have been relied upon to support land-use planning. Characteristics of sustainable land use, particularly compactness, contiguity, and compatibility, are discussed and how spatial optimization techniques have addressed these characteristics are detailed. In particular, objectives and constraints in spatial optimization approaches are examined

GIS and Network Analysis

Both geographic information systems (GIS) and network analysis are burgeoning fields, characterised by rapid methodological and scientific advances in recent years. A geographic information system (GIS) is a digital computer application designed for the capture, storage, manipulation, analysis and display of geographic information. Geographic location is the element that distinguishes geographic information from all other types of information. Without location, data are termed to be non-spatial and would have little value within a GIS. Location is, thus, the basis for many benefits of GIS: the ability to map, the ability to measure distances and the ability to tie different kinds of information together because they refer to the same place (Longley et al., 2001). GIS-T, the application of geographic information science and systems to transportation problems, represents one of the most important application areas of GIS-technology today. While traditional GIS formulation's strengths are in mapping display and geodata processing, GIS-T requires new data structures to represent the complexities of transportation networks and to perform different network algorithms in order to fulfil its potential in the field of logistics and distribution logistics. This paper addresses these issues as follows. The section that follows discusses data models and design issues which are specifically oriented to GIS-T, and identifies several improvements of the traditional network data model that are needed to support advanced network analysis in a ground transportation context. These improvements include turn-tables, dynamic segmentation, linear referencing, traffic lines and non-planar networks. Most commercial GIS software vendors have extended their basic GIS data model during the past two decades to incorporate these innovations (Goodchild, 1998). The third section shifts attention to network routing problems that have become prominent in GIS-T: the travelling salesman problem, the vehicle routing problem and the shortest path problem with time windows, a problem that occurs as a subproblem in many time constrained routing and scheduling issues of practical importance. Such problems are conceptually simple, but mathematically complex and challenging. The focus is on theory and algorithms for solving these problems. The paper concludes with some final remarks.