We consider definably compact groups in an o-minimal expansion of a real closed field. It is known that to each such group G is associated a natural exact sequence 1→ G00 → G → G/G00 → 1 where G00 is the “infinitesimal subgroup” of G and G/G00 is a compact real Lie group. We show that given a connected open subset U of G/G00 there is a canonical isomorphism between the fundamental group of U an...

Heuristics for combinatorial optimization are often controlled by discrete and continuous parameters that define its behavior. The number of possible configurations of the heuristic can be large, resulting in a difficult analysis. Manual tuning can be time-consuming, and usually considers a very limited number of configurations. An alternative to manual tuning is automatic tuning. In this paper...

The minimum-weight set cover problem is widely known to be O(log n)-approximable, with no improvement possible in the general case. We take the approach of exploiting problem structure to achieve better results, by providing a geometry-inspired algorithm whose approximation guarantee depends solely on an instance-specific combinatorial property known as shallow cell complexity (SCC). Roughly sp...

The Capacitated Vehicle Routing problem is a generalization of the Traveling Salesman problem in which a set of clients must be visited by a collection of capacitated tours. Each tour can visit at most Q clients and must start and end at a specified depot. We present the first approximation scheme for Capacitated Vehicle Routing for non-Euclidean metrics. Specifically we give a quasi-polynomial...

In this paper we consider the CAPACITATED DOMINATING SET problem — a generalisation of the DOMINATING SET problem where each vertex v is additionally equipped with a number c(v), which is the number of other vertices this vertex can dominate. We provide an algorithm that solves CAPACITATED DOMINATING SET exactly in O(1.89) time and polynomial space. Despite the fact that the CAPACITATED DOMINAT...

In this article we present benchmark datasets for the Mixed Capacitated Arc Routing Problem under Time restrictions with Intermediate Facilities (MCARPTIF). The problem is a generalisation of the Capacitated Arc Routing Problem (CARP), and closely represents waste collection routing. Four different test sets are presented, each consisting of multiple instance files, and which can be used to ben...

We consider a facility location problem to determine the points of dispensing medicine or supplies in a large-scale emergency. For this problem we consider capacitated facilities, a distance-dependent coverage function, and demand uncertainty. We formulate a special case of the maximal covering location problem (MCLP) with a loss function, to account for the distance-sensitive demand, and chanc...

We are interested in the design of robust (or resilient) capacitated rooted Steiner networks case terminals with uniform demands. Formally, we given a graph, capacity, and cost functions on edges, root, subset vertices called terminals, bound k $$ number possible edge failures. first study problem where = 1 k=1 network that want to must be tree covering root terminals: give complexity results p...

using greedy clustering method to solve capacitated location-routing problem with fuzzy demands abstract in this paper, the capacitated location routing problem with fuzzy demands (clrp_fd) is considered. in clrp_fd, facility location problem (flp) and vehicle routing problem (vrp) are observed simultaneously. indeed the vehicles and the depots have a predefined capacity to serve the customerst...