An efficient heuristic for calculating a protected path with specified nodes

The problem of determining a path between two nodes in a network that must visit specific intermediate nodes arises in a number of contexts. For example, one might require traffic to visit nodes where it can be monitored by deep packet inspection for security reasons. In this paper a new recursive heuristic is proposed for finding the shortest loopless path, from a source node to a target node, that visits a specified set of nodes in a network. In order to provide survivability to failures along the path, the proposed heuristic is modified to ensure that the calculated path can be protected by a node-disjoint backup path. The performance of the heuristic, calculating a path with and without protection, is evaluated by comparing with an integer linear programming (ILP) formulation for each of the considered problems. The ILP solver may fail to obtain a solution in a reasonable amount of time, especially in large networks, which justifies the need for effective, computationally efficient heuristics for solving these problems. Our numerical results are also compared with previous heuristics in the literature

The maximum disjoint paths problem on multi-relations social networks

Motivated by applications to social network analysis (SNA), we study the problem of finding the maximum number of disjoint uni-color paths in an edge-colored graph. We show the NP-hardness and the approximability of the problem, and both approximation and exact algorithms are proposed. Since short paths are much more significant in SNA, we also study the length-bounded version of the problem, in which the lengths of paths are required to be upper bounded by a fixed integer $l$. It is shown that the problem can be solved in polynomial time for $l=3$ and is NP-hard for $l\geq 4$. We also show that the problem can be approximated with ratio $(l-1)/2+\epsilon$ in polynomial time for any $\epsilon >0$. Particularly, for $l=4$, we develop an efficient 2-approximation algorithm

Fundamental schemes to determine disjoint paths for multiple failure scenarios

Disjoint path routing approaches can be used to cope with multiple failure cenarios. This can be achieved using a set of k (k>2) link- (or node-) disjoint path pairs (in single-cost and multi-cost networks). Alternatively, if Shared Risk Link Groups (SRLGs) information is available, the calculation of an SRLG-disjoint path pair (or of a set of such paths) can protect a connection against the joint failure of the set of links in any single SRLG. Paths traversing disaster-prone regions should be disjoint, but in safe regions it may be acceptable for the paths to share links or even nodes for a quicker recovery. Auxiliary algorithms for obtaining the shortest path from a source to a destination are also presented in detail, followed by the illustrated description of Bhandari’s and Suurballe’s algorithms for obtaining a pair of paths of minimal total additive cost. These algorithms are instrumental for some of the presented schemes to determine disjoint paths for multiple failure scenarios.info:eu-repo/semantics/publishedVersio

Extending Search Phases in the Micali-Vazirani Algorithm

The Micali-Vazirani algorithm is an augmenting path algorithm that offers the best theoretical runtime of O(n^{0.5} m) for solving the maximum cardinality matching problem for non-bipartite graphs. This paper builds upon the algorithm by focusing on the bottleneck caused by its search phase structure and proposes a new implementation that improves efficiency by extending the search phases in order to find more augmenting paths. Experiments on different types of randomly generated and real world graphs demonstrate this new implementation\u27s effectiveness and limitations

Multi-objective hierarchical algorithms for restoring Wireless Sensor Network connectivity in known environments

A Wireless Sensor Network can become partitioned due to node failure, requiring the deployment of additional relay nodes in order to restore network connectivity. This introduces an optimisation problem involving a tradeoff between the number of additional nodes that are required and the costs of moving through the sensor field for the purpose of node placement. This tradeoff is application-dependent, influenced for example by the relative urgency of network restoration. We propose a family of algorithms based on hierarchical objectives including complete algorithms and heuristics which integrate network design with path planning, recognising the impact of obstacles on mobility and communication. We conduct an empirical evaluation of the algorithms on random connectivity and mobility graphs, showing their relative performance in terms of node and path costs, and assessing their execution speeds. Finally, we examine how the relative importance of the two objectives influences the choice of algorithm. In summary, the algorithms which prioritise the node cost tend to find graphs with fewer nodes, while the algorithm which prioritise the cost of moving find slightly larger solutions but with cheaper mobility costs. The heuristic algorithms are close to the optimal algorithms in node cost, and higher in mobility costs. For fast moving agents, the node algorithms are preferred for total restoration time, and for slow agents, the path algorithms are preferred

Regenerator placement in optical networks

Cataloged from PDF version of article.Increase in the number of users and resources consumed by modern applications results in an explosive growth in the traffic on the Internet. Optical networks with higher bandwidths offer faster and more reliable transmission of data and allows transmission of more data. Fiber optical cables have these advantages over the traditional copper wires. So it is expected that optical networks will have a wide application area. However, there are some physical impairments and optical layer constraints in optical networks. One of these is signal degradation which limits the range of optical signals. Signals are degraded during transmission and below a threshold the signals become useless. In order to prevent this, regenerators which are capable of re-amplifying optical signals are used. Since regeneration is a costly process, it is important to decrease the number of regenerators used in an optical network. To increase the reliability of the network, two edge-disjoint paths between each terminal on the network are to be constructed. So the second path could be used in case of a failure in transmitting data on an edge of the first path. Considering these requirements, selecting the nodes on which regenerators are to be placed is an important decision. In this thesis, we discuss the problem of placing signal regenerators on optical networks with restoration. An integer linear program is formulated for this problem. Due to the huge size and other problems of the formulation, it is impractical to use it on large networks. For this reason, a fast heuristic algorithm is proposed to solve this problem. Three methods are proposed to check the feasibility when a fixed set of regenerators are placed on specific nodes. Additionally, a branch and bound algorithm which employs the proposed heuristic is developed to find the optimal solution of our problem. Performance of both the heuristics and the branch and bound method are evaluated in terms of number of regenerators placed and solution times of the algorithms.Özkök, OnurM.S

Routing with Reloads

We examine routing problems with reloads, how they can be modeled, their properties and how they can be solved. We propose a simple model, the Pickup and Delivery Problem with Reloads (RPDP), that captures the process of reloading and can be extended for real world applications. We present results that show that the RPDP is solvable in polynomial time if the number of requests is bounded by a constant. Additionally, we examine a special case of the RPDP, the k-Star Hub Problem. This problem is solvable efficiently by network flow approaches if no more than two hubs are available. Otherwise, it is NP-complete. In the second part of this thesis, additional constraints are incorporated into the model and a tabu search heuristic for this problem is presented. The heuristic has been implemented and tested on several benchmarking instances, both artificial and a real-world application. In the appendix, we discuss the application of column generation for a reload problem

Mission Planning Techniques for Cooperative LEO Spacecraft Constellations

This research develops a mission planning approach that allows different systems to cooperate in accomplishing a single mission goal. Using the techniques described allows satellites to cooperate in efficiently maneuvering, or collecting images of Earth and transmitting the collected data to users on the ground. The individual resources onboard each satellite, like fuel, memory capacity and pointing agility, are used in a manner that ensures the goals and objectives of the mission are realized in a feasible way. A mission plan can be generated for each satellite within the cooperating group that collectively optimize the mission objectives from a global viewpoint. The unique methods and framework presented for planning the spacecraft operations are flexible and can be applied to a variety of decision making processes where prior decisions impact later decision options. This contribution to the satellite constellation mission planning field, thus has greater applicability to the wider decision problem discipline