Min-max and min-max regret criteria are commonly used to define robust solutions. After motivating the use of these criteria, we present general results. Then, we survey complexity results for the min-max and min-max regret versions of some combinatorial optimization problems: shortest path, spanning tree, assignment, cut, s-t cut, knapsack. Since most of these problems are NP-hard, we also inv...

Min-max and min-max regret criteria are commonly used to define robust solutions. After motivating the use of these criteria, we present general results. Then, we survey complexity results for the min-max and min-max regret versions of some combinatorial optimization problems: shortest path, spanning tree, assignment, cut, s-t cut, knapsack. Since most of these problems are NP-hard, we also inv...

The shortest path problem in which the (s, t)-paths P of a given digraph G = (V,E) are compared with respect to the sum of their edge costs is one of the best known problems in combinatorial optimization. The paper is concerned with a number of variations of this problem having different objective functions like bottleneck, balanced, minimum deviation, algebraic sum, k-sum and k-max objectives,...

The multi-criteria shortest path problem is concerned with the minimization of multiple, possibly conflicting objectives such as travel time and highway tolls. Sanders and Mandow [60] present a parallel algorithm for this problem. They generalize Dijkstra’s [18] single-criterion shortest path algorithm to multiple criteria, while parallelizing all additional work induced by this generalization....

In this paper, we introduce a distributed algorithm for single source shortest path problem for undirected graphs. In this problem, we find the shortest path from a given source node to other nodes in the graph. We start with undirected unweighted graphs in which the shortest path is a path with minimum number of edges. Following, we modify the algorithm to find shortest path for weighted graph...