Libertad Tansini

Overlaps help: Improved bounds for group testing with interval queries

Given a finite ordered set of items and an unknown distinguished subset P of up to p positive elements, identify the items in P by asking the least number of queries of the type does the subset Q intersect P?, where Q is a subset of consecutive elements of {1,2,...,n}. This problem arises, e.g., in computational biology, in a particular method for determining splice sites in genes. We consider time-efficient algorithms where queries are arranged in a fixed number s of stages: In each stage, queries are performed in parallel. In a recent bioinformatics paper, we proved optimality (subject to lower-order terms) with respect to the number of queries, of some strategies for the special cases p=1 or s=2. Exploiting new ideas, we are now able to provide improved lower bounds for any p>=2 and s>=3 and improved upper bounds for larger s. Most notably, our new bounds converge as s grows. Our new query scheme uses overlapping query intervals within a stage, which is effective for large enough s. This contrasts with our previous results for s= =3. Anyway, the remaining gaps between the current upper and lower bounds for any fixed s>=3 amount to small constant factors in the main term. The paper ends with a discussion of practical implications in the case that the positive elements are well separated.

New measures of proximity for the assignment algorithms in the MDVRPTW

This paper proposes new proximity measures for assignment algorithms for the Multi-Depot Vehicle Routing Problem with Time Windows (MDVRPTW). Given the intrinsic difficulty of this problem class, two-step approximation methods of the type ‘cluster first, route second’ seem to be the most promising for practical size problems. The focus is on the clustering phase, the assignment of customers to depots. Our approach is to extend the existing metrics with time windows. New measures that include time windows and distances are added to two assignment heuristics, that previously only used distance to evaluate proximity between customers and depots. A computational study of their performance is presented, which shows that the inclusion of time windows in the measures of proximity gives better results, in terms of routing, than only using the distance.

Probabilistic analysis for a multiple depot vehicle routing problem

We give the first probabilistic analysis of the Multiple Depot Vehicle Routing Problem(MDVRP) where we are given k depots and n customers in [0,1]2. The optimization problem is to find a collection of disjoint TSP tours with minimum total length such that all customers are served and each tour contains exactly one depot(not all depots have to be used). In the random setting the depots as well as the customers are given by independently and uniformly distributed random variables in [0,1]2. We show that the asymptotic tour length is

Monte Carlo mirror algorithm for the port-of-entry inspection problem

alpha_{k} sqrt{n}

A Multi-Tree Committee to Assist Port-of-entry Inspection Decisions

for some constant αk depending on the number of depots. If k=o(n), αk is the constant α(TSP) of the TSP problem. Beardwood, Halton, and Hammersley(1959) showed 0.62≤ α(TSP)≤ 0.93. For k=λn, λ>0, one expects that with increasing λ the MDVRP tour length decreases. We prove that this is true exhibiting lower and upper bounds on αk, which decay as fast as

Overlaps Help: Improved Bounds for Group Testing with Interval Queries

(1+lambda)^{-frac{1}{2}}

Sistema de información para gestión de riesgos en Uruguay

. n nA heuristics which first clusters customers around the nearest depot and then does the TSP routing is shown to find an optimal tour almost surely.

LOGÍSTICA HUMANITARIA Y SU APLICACIÓN EN URUGUAY

A naive exhaustive manual inspection of port-of-entry is the most secure inspection policy. However, the number of within containers allows only to check a limited number of containers each day. The aim of this paper is to offer an automatic, simple and intuitive algorithm to select which containers should be inspected, following a given training set of classifications as close as possible. We prove that there exists an optimal deterministic inspection policy for the classification problem, called mirror solution. Inspired by the strength of Monte Carlo-based methods for simulation of rare events, we add randomisation to the mirror solution. We first show that the randomised mirror solution is useful in practice and computationally efficient, since it depends linearly on the size of the training set, for a given number of sensors and risk levels. Finally, we present the results of the proposed port-of-entry inspection policy in a real-life scenario.

LOGÍSTICA HUMANITARIA Y SU

A natural way to avoid the injection of potentially dangerousor illicit products in a certain country is by means of protection, following a strict port-of-entry inspection policy. A naive exhaustive manual inspection is the most secure policy. However, the number of within containers allows only to check a limited number of containers by day. As a consequence, a smart port-of-entry selection policy must trade cost of inspection with security, in order to fit into the dynamic operation of a port.

Mining Web Logs to Improve User Experience in Web Search

Given a finite ordered set of items and an unknown distinguished subset P of up to p positive elements, identify the items in P by asking the least number of queries of the type does the subset Q intersect P?, where Q is a subset of consecutive elements of {1, 2, ..., n}. This problem arises e.g. in computational biology, in a particular method for determining splice sites. We consider time-efficient algorithms where queries are arranged in a fixed number s of stages: in each stage, queries are performed in parallel. In a recent paper we devised query-optimal strategies in the special cases p=1 or s=2, subject to lower-order terms. Exploiting new ideas we are now able to provide a much neater argument that allows doubling the general lower bound for any pi¾? 2 and si¾? 3. Moreover, we provide new strategies that match this new bound up to the constant of the main term. The new query scheme shows an effective use of overlapping queries within a stage. Remarkably, this contrasts with the known results for s ≤ 2 where optimal strategies were implemented by disjoint queries.