Nicolas Catusse

Fixed-Parameter Algorithms for Rectilinear Steiner tree and Rectilinear Traveling Salesman Problem in the plane

Abstract Given a set P of n points with their pairwise distances, the traveling salesman problem (TSP) asks for a shortest tour that visits each point exactly once. A TSP instance is rectilinear when the points lie in the plane and the distance considered between two points is the l1 distance. In this paper, a fixed-parameter algorithm for the Rectilinear TSP is presented and relies on techniques for solving TSP on bounded-treewidth graphs. It proves that the problem can be solved in O(nh7h) where h ≤ n denotes the number of horizontal lines containing the points of P. The same technique can be directly applied to the problem of finding a shortest rectilinear Steiner tree that interconnects the points of P providing a O(nh5h) time complexity. Both bounds improve over the best time bounds known for these problems.

Bidirected minimum Manhattan network problem

In the bidirected minimum Manhattan network problem, given a set T of n terminals in the plane, no two terminals on the same horizontal or vertical line, we need to construct a network N(T) of minimum total length with the property that the edges of N(T) belong to the axis-parallel grid defined by T and are oriented in a such a way that every ordered pair of terminals is connected in N(T) by a directed Manhattan path. In this article, we present a polynomial factor 2-approximation algorithm for the bidirected minimum Manhattan network problem.

Client selection and combination for farm perishable products

Abstract This paper deals with the problem of selecting the most profitable combination of clients to sell a given perishable production of a vegetable farm. A farmer has pre-qualified a pool of potential clients, characterized by specific product mixes, prices, supply contract durations and farm workers requirements to prepare and deliver the order. The farmer is allowed to purchase products from surrounding farms to meet the contracts specifications, if the farm production is not sufficient. We present a Mixed Integer Linear Programming model to maximize the profit of farm sales with production and workforce capacities. We develop submodels to describe the demand characteristics of four targeted clients categories: farmers’ market, community supported agriculture, contract demand and wholesalers. Theoretical complexity of the model and preliminary computational results are discussed.

SPOT: an optimization software for dynamic observation programming

The surveys dedicated to the search for extrasolar planets with the recently installed extreme-AO, high contrast Planet Imagers generally include hundreds of targets, to be observed sometimes repeatedly, generally in Angular Differential Imaging Mode. Each observation has to fulfill several time-dependent constraints, which makes a manual elaboration of an optimized planning impossible. We have developed a software (SPOT), an easy to use tool with graphical interface that allows both long term (months, years) and dynamic (nights) optimized scheduling of such surveys, taking into account all relevant constraints. Tests show that excellent schedules and high filling efficiencies can be obtained with execution times compatible with real-time scheduling, making possible to take in account complex constraints and to dynamically adapt planning to unexpected circumstances even during their execution. Moreover, such a tool is very valuable during survey preparations to build target lists and calendars. SPOT could be easily adapted for scheduling observations other instruments or telescopes.