So far we have studied the set covering problem, but not looked at any real life applications. The shortest superstring problem takes as input, several strings of different lengths and finds the shortest string that contains all the input strings as substrings. This is helpful in the genome project since it will allow researchers to determine entire coding regions from a collection of fragmente...

The shortest path problem is one of the most fundamental problems in network optimization. This paper is concerned with shortest path problems in non-deterministic environment, in which the lengths of some arcs have stochastic characteristics and meanwhile some have uncertain characteristics. In order to investigate paths in these networks, this paper introduces the chance distribution of minim...

The shortest path problem is among the most fundamental combinatorial optimization problems to answer reach-ability queries. A single pair shortest path computation using Dijkstra’s algorithm requires few seconds on a very large social network. Many traversal algorithms imply precomputed information to speed up the runtime query process. However, computing effective auxiliary data in a reasonab...

In this paper we consider a variant of the multi-criteria shortest path problem where the different criteria are combined in an arbitrary conic combination at query time. We show that contraction hierarchies (CH) a very powerful speedup technique originally developed for standard shortest path queries (Geisberger et al. 2008) can be adapted to this scenario and lead after moderate preprocessing...

In this paper we consider a variant of the multi-criteria shortest path problem where the different criteria are combined in an arbitrary conic combination at query time. We show that contraction hierarchies (CH) a very powerful speedup technique originally developed for standard shortest path queries (Geisberger et al. 2008) can be adapted to this scenario and lead after moderate preprocessing...

It is well known that the Steiner minimal tree problem is one of the classical nonlinear combinatorial optimization problems. A visualization experiment approach succeeds in generating Steiner points automatically and showing the system shortest path, named Steiner minimum tree, physically and intuitively. However, it is difficult to form stabilized system shortest path when the number of given...

k-Interval Routing Scheme (k-IRS) is a compact routing method that allows up to k interval labels to be assigned to an arc. A fundamental problem is to characterize the networks that admit k-IRS. All of the problems related to single-shortest-path k-IRS have already been shown to be NP-complete. For all-shortest-path k-IRS, the characterization problems have been proved to be NP-complete for ev...

We introduce the universal shortest path problem (Univ-SPP) which generalizes both classical and new shortest path problems. Starting with the definition of the even more general universal combinatorial optimization problem (UnivCOP), we show that a variety of objective functions for general combinatorial problems can be modeled if all feasible solutions have the same cardinality. Since this as...

The article studies the generalisation of the maximum flow of minimum cost problem for the case of maximum discrete dynamic flow of minimum travelling cost and travelling time. The approach is based on iteratively generating efficient extreme points in the objective space by solving a series of single objective maximum flow problems with different objective functions. On each of the iterations,...

Demand-robust versions of common optimization problems were recently introduced by Dhamdhere et al. [4] motivated by the worst-case considerations of two-stage stochastic optimization models. We study the demand robust min-cut and shortest path problems, and exploit the nature of the robust objective to give improved approximation factors. Specifically, we give a (1 + √ 2) approximation for rob...