The winter road maintenance arc-routing is recognized as a notoriously hard problem not only from the algorithmic point of view. This paper lays down foundations theoretical understanding our new optimization for Plzeň region Czech Republic which has been implemented by regional authorities since 2019–20. Our approach not, contrary to most existing work, based on integer and linear programming ...

It is well-known that the tight lower bounds determine the effectiveness of the brancn and bound method for the NP-hard problems. In this paper, we present a new lower bounding procedure for the capacitated arc routing problem (CARP), one of the arc routing problems. They give the tight lower bounds and it is easy to develop an exact algorithm usinl~ their network structures.

Arc routing problems arise, for example, when roads require treatment or customers must be served who are located along roads. So practical examples include the routing of people or vehicles for postal deliveries, meter reading and winter gritting, where the roads need to be treated with salt or some other agent to prevent the surface becoming icy. An arc routing problem is represented by a gra...

In Arc Routing Problems, ARPs, the aim is to find on a graph a minimum cost traversal satisfying some conditions related to the links of the graph. Due to restrictions to traverse some streets in a specified way, most applications of ARPs must be modeled with a mixed graph. Although several exact algorithms have been proposed, no polyhedral investigations have been done for ARPs on a mixed grap...

We study a class of Cayley graphs as models for interconnection networks. With focus on efficient communication we prove that for any graph in the class there exists a gossiping protocol which exhibits attractive features, and moreover we give an algorithm for constructing such a protocol. In particular, these hold for two important subclasses of graphs, namely, Cayley graphs admitting a comple...

Internet protocol (IP) traffic follows rules established by routing protocols. Shortest path based protocols, such as Open Shortest Path First (OSPF), direct traffic based on arc weights assigned by the network operator. Each router computes shortest paths and creates destination tables used for routing flow on the shortest paths. If a router has multiple outgoing links on shortest paths to a g...