We study the problem of finding small integer arc lengths in a digraph such that some given paths are uniquely determined shortest paths. This Inverse Shortest Paths (ISP) problem arises in the planning of shortest path networks. We present an O(|V |)-approximation algorithm for ISP and show that minimizing the longest arc or the longest path length is APX -hard. Thus, deciding if a given path ...

This article deals with the intermodal transportation problem for the commodities delivery between different locations. The time – dependent shortest path planning, in which the travel time along each arc is a known function of the departure time along the arc, is a very important problem and arises in many practical application such as a routing system of a container used in the time – depende...

We present and analyze a fully dynamic algorithm for maintaining minimum cost directed spanning forests (branchings) in the presence of arc deletions and insertions. We provide algorithms that maintain a data structure, when an arc is deleted from or inserted in the digraph. Queries to the data structure for the optimum branching are answered in O(n) time, while the cost of an optimum branching...

We consider a network design problem which has shortest routing restriction based on the values determined by the installed facilities on each arc. In conventional multicommodity network design problem, a commodity can be routed through any possible path when the capacity is available. But, we consider a problem in which the commodity between two nodes must be routed on a path which has shortes...

We study a variant of the capacitated vehicle routing problem where the cost over each arc is defined as the product of the arc length and the weight of the vehicle when it traverses that arc. We propose two new mixed integer linear programming formulations for the problem: an arc-load formulation and a set partitioning formulation based on q-routes with additional constraints. A family of cycl...

The problem of minimum cost routing has been extensively explored in a variety of contexts. While there is a prevalence of routing applications based on least distance, time, and related attributes, exertion-based routing has remained relatively unexplored. In particular, the network structures traditionally used to construct minimum cost paths are not suited to representing exertion or finding...

We provide a flexible graph architecture, and an implementation of solvers to some of the most ubiquitous problems in the field of Arc Routing, (The Chinese Postman Problem on undirected, directed, mixed, and windy graphs, as well as the Rural Postman Problem on directed and windy graphs). The project is completed in java, is open source, and is hosted at https://github.com/Olibear/ArcRoutingLi...

In this paper we consider the Capacitated Arc Routing Problem with Time windows. We suggest two algorithms for solving the problem to optimality and a heuristic for obtaining high quality solutions. To our knowledge this is the first paper to consider optimal solution

Given a directed graph with capacities on each arc and given a set of commodities, the QoS constrained Routing Problem (QCRP) consists in routing each commodity while respecting a endto-end upper bound on the delay for each packet. This problem is NP-hard and we propose an augmented Lagrangean approach to solve it. A flow deviation algorithm as well as a projected gradient method are proposed t...

When people choose routes minimizing their individual delay, the aggregate congestion can be much higher compared to that experienced by a centrally-imposed routing. Yet centralized routing is incompatible with presence of self-interested users. How we reconcile two? In this paper address question within repeated game framework and propose fair incentive mechanism based on artificial currencies...