Package Delivery Using Drones with Restricted Movement Areas

For the problem of delivering a package from a source node to a destination node in a graph using a set of drones, we study the setting where the movements of each drone are restricted to a certain subgraph of the given graph. We consider the objectives of minimizing the delivery time (problem DDT) and of minimizing the total energy consumption (problem DDC). For general graphs, we show a strong inapproximability result and a matching approximation algorithm for DDT as well as NP-hardness and a 2-approximation algorithm for DDC. For the special case of a path, we show that DDT is NP-hard if the drones have different speeds. For trees, we give optimal algorithms under the assumption that all drones have the same speed or the same energy consumption rate. The results for trees extend to arbitrary graphs if the subgraph of each drone is isometric

Mathematical programming models for scheduling locks in sequence

We investigate the scheduling of series of consecutive locks. This setting occurs naturally along canals and waterways. We describe a problem that generalizes different models that have been studied in literature. Our contribution is to (i) provide two distinct mathematical programming formulations, and compare them empirically, (ii) show how these models allow for minimizing emission by having the speed of a ship as a decision variable, (iii) to compare, on realistic instances, the optimum solution found by solving the models with the outcome of a decentralized heuristic

Approximation algorithms for multi-dimensional assignment problems with decomposable costs

AbstractThe k-dimensional assignment problem with decomposable costs is formulated as follows. Given is a complete k-partite graph G = (X0 ∪ ⋯ ∪ Xk − 1, E), with |Xi| = p for each i, and a nonnegative length function defined on the edges of G. A clique of G is a subset of vertices meeting each Xi in exactly one vertex. The cost of a clique is a function of the lengths of the edges induced by the clique. Four specific cost functions are considered in this paper; namely, the cost of a clique is either the sum of the lengths of the edges induced by the clique (sum costs), or the minimum length of a spanning star (star costs) or of a traveling salesman tour (tour costs) or of a spanning tree (tree costs) of the induced subgraph. The problem is to find a minimum-cost partition of the vertex set of G into cliques. We propose several simple heuristics for this problem, and we derive worst-case bounds on the ratio between the cost of the solutions produced by these heuristics and the cost of an optimal solution. The worst-case bounds are stated in terms of two parameters, viz. k and τ, where the parameter τ indicates how close the edge length function comes to satisfying the triangle inequality

Counting and enumerating aggregate classifiers

peer reviewedaudience: researcherWe propose a generic model for the "weighted voting" aggregation step performed by several methods in supervised classification. Further, we construct an algorithm to count the number of distinct aggregate classifiers that arise in this model. When there are only two classes in the classification problem, we show that a class of functions that arises from aggregate classifiers coincides with the class of self-dual positive threshold Boolean functions

Identifying optimal strategies in Kidney Exchange games is Σ2p-complete

In Kidney Exchange Games, agents (e.g. hospitals or national organizations) have control over a number of incompatible recipient-donor pairs whose recipients are in need of a transplant. Each agent has the opportunity to join a collaborative effort which aims to maximize the total number of transplants that can be realized. However, the individual agent is only interested in maximizing the number of transplants within the set of recipients under its control. Then, the question becomes: which recipient-donor pairs to submit to the collaborative effort? We model this situation by introducing the Stackelberg Kidney Exchange Game, a game where an agent, having perfect information, needs to identify a strategy, i.e., to decide which recipient-donor pairs to submit. We show that even in this simplified setting, identifying an optimal strategy is Σ2p-complete, whenever we allow exchanges involving at most a fixed number K≥ 3 pairs. However, when we restrict ourselves to pairwise exchanges only, the problem becomes solvable in polynomial time.</p