2,311 research outputs found
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 . It is shown that the problem can be solved in
polynomial time for and is NP-hard for . We also show that the
problem can be approximated with ratio in polynomial time
for any . Particularly, for , we develop an efficient
2-approximation algorithm
Edge- and Node-Disjoint Paths in P Systems
In this paper, we continue our development of algorithms used for topological
network discovery. We present native P system versions of two fundamental
problems in graph theory: finding the maximum number of edge- and node-disjoint
paths between a source node and target node. We start from the standard
depth-first-search maximum flow algorithms, but our approach is totally
distributed, when initially no structural information is available and each P
system cell has to even learn its immediate neighbors. For the node-disjoint
version, our P system rules are designed to enforce node weight capacities (of
one), in addition to edge capacities (of one), which are not readily available
in the standard network flow algorithms.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005
SAT Modulo Monotonic Theories
We define the concept of a monotonic theory and show how to build efficient
SMT (SAT Modulo Theory) solvers, including effective theory propagation and
clause learning, for such theories. We present examples showing that monotonic
theories arise from many common problems, e.g., graph properties such as
reachability, shortest paths, connected components, minimum spanning tree, and
max-flow/min-cut, and then demonstrate our framework by building SMT solvers
for each of these theories. We apply these solvers to procedural content
generation problems, demonstrating major speed-ups over state-of-the-art
approaches based on SAT or Answer Set Programming, and easily solving several
instances that were previously impractical to solve
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
Combinatorial Path Planning for a System of Multiple Unmanned Vehicles
In this dissertation, the problem of planning the motion of m Unmanned Vehicles (UVs) (or simply vehicles) through n points in a plane is considered. A motion plan for a vehicle is given by the sequence of points and the corresponding angles at which each point must be visited by the vehicle. We require that each vehicle return to the same initial location(depot) at the same heading after visiting the points. The objective of the motion planning problem is to choose at most q(≤ m) UVs and find their motion plans so that all the points are visited and the total cost of the tours of the chosen vehicles is a minimum amongst all the possible choices of vehicles and their tours. This problem is a generalization of the wellknown Traveling Salesman Problem (TSP) in many ways: (1) each UV takes the role of salesman (2) motion constraints of the UVs play an important role in determining the cost of travel between any two locations; in fact, the cost of the travel between any two locations depends on direction of travel along with the heading at the origin and destination, and (3) there is an additional combinatorial complexity stemming from the need to partition the points to be visited by each UV and the set of UVs that must be employed by the mission.
In this dissertation, a sub-optimal, two-step approach to motion planning is presented to solve this problem:(1) the combinatorial problem of choosing the vehicles and their associated tours is based on Euclidean distances between points and (2) once the sequence of points to be visited is specified, the heading at each point is determined based on a Dynamic Programming scheme. The solution to the first step is based on a generalization of Held-Karp’s method. We modify the Lagrangian heuristics for finding a close sub-optimal solution.
In the later chapters of the dissertation, we relax the assumption that all vehicles are homogenous. The motivation of heterogenous variant of Multi-depot, Multiple Traveling Salesmen Problem (MDMTSP) derives form applications involving Unmanned Aerial Vehicles (UAVs) or ground robots requiring multiple vehicles with different capabilities to visit a set of locations
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