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

Protected shortest path visiting specified nodes

In this paper heuristics are proposed for finding the shortest loopless path, from a source node to a target node, that visits a given set of nodes in a directed graph, such that it can be protected using a node-disjoint path. This type of problem may arise due to network management constraints. The problem of calculating the shortest path that visits a given set of nodes is at least as difficult as the traveling salesman problem, and it has not received much attention. Nevertheless an efficient integer linear programming (ILP) formulation has been recently proposed for this problem. Here, the ILP formulation is adapted to include the constraint that the obtained path will be able to be protected by a node-disjoint path. Computational experiments show that this approach, namely in large networks, may fail to obtain a solution in a reasonable amount of time. Therefore three versions of a heuristic are proposed, for which extensive computational results show that they are able to find a solution in most cases, and that the calculated solutions present an acceptable relative error regarding the cost of the optimal active path. Further the CPU time required by the heuristics is significantly smaller than the required by the used ILP solver