Class Of Network Design Problems Research Articles

Node-Connectivity Terminal Backup, Separately Capacitated Multiflow, and Discrete Convexity

The terminal backup problems ([E. Anshelevich and A. Karagiozova, SIAM J. Comput., 40 (2011), pp. 678–708]) form a class of network design problems: Given an undirected graph with a requirement on terminals, the goal is to find a minimum-cost subgraph satisfying the connectivity requirement. The node-connectivity terminal backup problem requires a terminal to connect other terminals with a number of node-disjoint paths. This problem is not known whether is NP-hard or tractable. Fukunaga [SIAM J. Discrete Math., 30 (2016), pp. 777–800] gave a -approximation algorithm based on an LP-rounding scheme using a general LP-solver. In this paper, we develop a combinatorial algorithm for the relaxed LP to find a half-integral optimal solution in time, where is the number of nodes, is the number of edges, is the number of terminals, is the maximum edge-cost, is the maximum edge-capacity, and is the time complexity of a max-flow algorithm in a network with nodes and edges. The algorithm implies that the -approximation algorithm for the node-connectivity terminal backup problem is also efficiently implemented. For the design of algorithm, we explore a connection between the node-connectivity terminal backup problem and a new type of a multiflow, which is called a separately capacitated multiflow. We show a min-max theorem which extends the Lovász–Cherkassky theorem to the node-capacity setting. Our results build on discrete convexity in the node-connectivity terminal backup problem.

Distance Transformation for Network Design Problems

We propose a new generic way to construct extended formulations for a large class of network design problems with given connectivity requirements. The approach is based on a graph transformation th...

Network design for minimum spanning trees under Hamming distance

We consider a class of network-design problems with minimum sum of modification and network costs for minimum spanning trees under Hamming distance. By constructing three auxiliary networks, we present a strongly polynomial-time algorithm for this problem. The method can be applied to solve many network-design problems. And, we show that a variation model of this problem is NP-hard, even when the underlying network is a tree, by transforming the 0–1 knapsack problem to this model. doi:10.1017/S1446181117000116

NETWORK DESIGN FOR MINIMUM SPANNING TREES UNDER HAMMING DISTANCE

We consider a class of network-design problems with minimum sum of modification and network costs for minimum spanning trees under Hamming distance. By constructing three auxiliary networks, we present a strongly polynomial-time algorithm for this problem. The method can be applied to solve many network-design problems. And, we show that a variation model of this problem is NP-hard, even when the underlying network is a tree, by transforming the 0–1 knapsack problem to this model.

Stabilizing branch‐and‐price for constrained tree problems

AbstractWe consider a rather generic class of network design problems in which a set or subset of given terminal nodes must be connected to a dedicated root node by simple paths and a variety of resource and/or quality of service constraints must be respected. These extensions of the classical Steiner tree problem on a graph can be well modeled by a path formulation in which individual variables are used for all feasible paths. To solve this formulation in practice, branch‐and‐price is used. It turns out, however, that a naive implementation of column generation suffers strongly from certain degeneracies of the pricing subproblem, leading to excessive running times. After analyzing these computational problems, we propose two methods to accelerate and stabilize column generation by using alternative dual‐optimal solutions. The resulting branch‐and‐price approach is practically tested on the rooted delay‐constrained Steiner tree problem and a quota‐constrained version of it. Results indicate that the proposed methods in general speed‐up the solution process dramatically, far more than a piecewise linear stabilization to which we compare. Furthermore, our branch‐and‐price approach exhibits on most test instances a better performance than a state‐of‐the‐art branch‐and‐cut approach based on layered graphs. As the new stabilization technique utilizing alternative dual‐optimal solutions is generic in the sense that it easily adapts to the inclusion of a large variety of further constraints and different objective functions, the proposed method is highly promising for a large class of network design problems. © 2012 Wiley Periodicals, Inc. NETWORKS, 2013

Routing and network design with robustness to changing or uncertain traffic demands

A new class of network design problems were introduced by Fingerhut et al. [26], and independently by Duffield et al. [20], to address, among other things, the issue of uncertainty in the demand matrix. The so-called hose model (the term was coined in [20]) for demand matrices from [26, 20] was subsequently generalized to the polyhedral model by Ben-Ameur and Kerivin [11, 10]. In a different direction, Räacke [51] showed the existence of good randomized oblivious routings in all undirected graphs. This was followed by a proof of the polynomial time solvability of an optimal oblivious routing scheme [7]. One can view the above developments in a common framework of robust optimization. We give a survey of these developments and related work with the aim of providing a unified picture. We also highlight the remaining open problems.

An approximation algorithm for network design problems with downwards-monotone demand functions

Building on an existing 2-approximate algorithm for the class of network design problems with downwards-monotone demand functions, many of which are NP-hard, we present an algorithm that produces solutions that are at least as good as and typically better than solutions produced by the existing algorithm.

Conceptual Model Of The Convergent Multistation Network Configuration Task

Despite the potential of close range photogrammetry for high accuracy measurement, it has rarely been used by other than experienced photogrammetrists. One major contributing factor is the expertise needed to design multistation sensor configurations. This paper presents a conceptual model for the most fundamental task in this design problem, configuring a first approximation to a strong imaging geometry. This task entails making decisions on the number of camera stations needed and where they should be placed (positioned and oriented). The conceptual model is based on the theory of generic networks. A generic network constitutes compiled expertise, describing an ideal configuration of camera stations that can be employed to provide a strong imaging geometry for a class of network design problems. In addition to improving our understanding of cognition in network design, this model performs an important role in the development of an expert system for automated network design for dimensional inspection tasks.

State-dependent queueing models in emergency evacuation networks

Planning and design of evacuation networks is both a complex and critically important problem for a number of emergency situations. One particularly critical class of examples concerns the emergency evacuation of chemical plants, high-rise buildings, and naval vessels due to fire, explosion or other emergency. The problem is a highly transient, stochastic, nonlinear, integer programming problem and previous methodologies utilizing queueing network models have proved useful in the design of emergency evacuation plans. We enhance this class of queueing network models by adding state-dependent queueing models to capture the nonlinear effects of increased occupant traffic flow along emergency evacuation routes. A mean value analysis algorithm and computational experience of the methodology illustrates our model's usefulness for this class of network design problems.

Network Design for a Large Class of Teleconferencing Systems

This paper introduces a new class of network design problems implementing an integrated teleconferencing environment consisting of a video space showing images of the participants, an audio space providing their voices, and a graphics space providing reference and discussion material for the conference. These various spaces provide services of differing quality and type. The problem posed is to design topologically optimal networks that are least costly and that will have the flexibility to carry conferences of differing service quality and type. The actual networks studied in this paper consist of the design of a private network for a single conference among N identical, but arbitrarily located, sites. Network designs will be minimum link-cost or constrained minimum link-cost optimal, where the first is minimal over all possible network topologies and the second is constrained to consider only those topologies that have the minimum number of links. For terrestrial systems, one of the interesting results is that classical network topologies such as rings and minimum spanning trees are optimal for some conference types. However, no topology is optimal for all types, and some topologies use their capacity very poorly when used for a type for which they were not optimized. Unlike terrestrial networks, satellite networks may be easily configured to have all of their capacity available for all conference types.