Approximability results for stable marriage problems with ties

We consider instances of the classical stable marriage problem in which persons may include ties in their preference lists. We show that, in such a setting, strong lower bounds hold for the approximability of each of the problems of finding an egalitarian, minimum regret and sex-equal stable matching. We also consider stable marriage instances in which persons may express unacceptable partners in addition to ties. In this setting, we prove that there are constants delta, delta' such that each of the problems of approximating a maximum and minimum cardinality stable matching within factors of delta, delta' (respectively) is NP-hard, under strong restrictions. We also give an approximation algorithm for both problems that has a performance guarantee expressible in terms of the number of lists with ties. This significantly improves on the best-known previous performance guarantee, for the case that the ties are sparse. Our results have applications to large-scale centralized matching schemes

General Scheme for Perfect Quantum Network Coding with Free Classical Communication

This paper considers the problem of efficiently transmitting quantum states through a network. It has been known for some time that without additional assumptions it is impossible to achieve this task perfectly in general -- indeed, it is impossible even for the simple butterfly network. As additional resource we allow free classical communication between any pair of network nodes. It is shown that perfect quantum network coding is achievable in this model whenever classical network coding is possible over the same network when replacing all quantum capacities by classical capacities. More precisely, it is proved that perfect quantum network coding using free classical communication is possible over a network with $k$ source-target pairs if there exists a classical linear (or even vector linear) coding scheme over a finite ring. Our proof is constructive in that we give explicit quantum coding operations for each network node. This paper also gives an upper bound on the number of classical communication required in terms of $k$, the maximal fan-in of any network node, and the size of the network.Comment: 12 pages, 2 figures, generalizes some of the results in arXiv:0902.1299 to the k-pair problem and codes over rings. Appeared in the Proceedings of the 36th International Colloquium on Automata, Languages and Programming (ICALP'09), LNCS 5555, pp. 622-633, 200

Technological and environmental risks in the context of climate change.

Considering the importance of the debate on the topic of disasters related to landslides, flooding and technological risks, under international and more recently in Brazil, this work analyzes the situations of vulnerability risk areas on the Northern Coast of São Paulo. The situation analyzed refers to the effects of the implementation of large infrastructure projects related to oil and gas on the occupation of risk areas to landslides and flooding, besides considering the technological risks inherent in these megaprojects. Figure 1 show the technological and environmental risks in three regions of Brazilian Southeast coast ? detailed to Northern coast of São Paulo

An Exact Algorithm for TSP in Degree-3 Graphs via Circuit Procedure and Amortization on Connectivity Structure

The paper presents an O^*(1.2312^n)-time and polynomial-space algorithm for the traveling salesman problem in an n-vertex graph with maximum degree 3. This improves the previous time bounds of O^*(1.251^n) by Iwama and Nakashima and O^*(1.260^n) by Eppstein. Our algorithm is a simple branch-and-search algorithm. The only branch rule is designed on a cut-circuit structure of a graph induced by unprocessed edges. To improve a time bound by a simple analysis on measure and conquer, we introduce an amortization scheme over the cut-circuit structure by defining the measure of an instance to be the sum of not only weights of vertices but also weights of connected components of the induced graph.Comment: 24 pages and 4 figure

Approximation algorithms for hard variants of the stable marriage and hospitals/residents problems

When ties and incomplete preference lists are permitted in the Stable Marriage and Hospitals/Residents problems, stable matchings can have different sizes. The problem of finding a maximum cardinality stable matching in this context is known to be NP-hard, even under very severe restrictions on the number, size and position of ties. In this paper, we describe polynomial-time 5/3-approximation algorithms for variants of these problems in which ties are on one side only and at the end of the preference lists. The particular variant is motivated by important applications in large scale centralised matching schemes

Multiscale approaches to analyse risks and vulnerabilities in the coastal zone (Brazil).

The objectives of this work were: (i) identified the risk areas of landslides, flooding and sea level rise and social vulnerabilities in different scales of analysis; (ii) analyse the risk perception of people living in this risk areas; (iii) found a common dialogues between sciences and communities to inform policy and decision-making in the different socioeconomic sectors