Matroid Online Bipartite Matching and Vertex Cover

The Adwords and Online Bipartite Matching problems have enjoyed a renewed attention over the past decade due to their connection to Internet advertising. Our community has contributed, among other things, new models (notably stochastic) and extensions to the classical formulations to address the issues that arise from practical needs. In this paper, we propose a new generalization based on matroids and show that many of the previous results extend to this more general setting. Because of the rich structures and expressive power of matroids, our new setting is potentially of interest both in theory and in practice. In the classical version of the problem, the offline side of a bipartite graph is known initially while vertices from the online side arrive one at a time along with their incident edges. The objective is to maintain a decent approximate matching from which no edge can be removed. Our generalization, called Matroid Online Bipartite Matching, additionally requires that the set of matched offline vertices be independent in a given matroid. In particular, the case of partition matroids corresponds to the natural scenario where each advertiser manages multiple ads with a fixed total budget. Our algorithms attain the same performance as the classical version of the problems considered, which are often provably the best possible. We present $1-1/e$-competitive algorithms for Matroid Online Bipartite Matching under the small bid assumption, as well as a $1-1/e$-competitive algorithm for Matroid Online Bipartite Matching in the random arrival model. A key technical ingredient of our results is a carefully designed primal-dual waterfilling procedure that accommodates for matroid constraints. This is inspired by the extension of our recent charging scheme for Online Bipartite Vertex Cover.Comment: 19 pages, to appear in EC'1

The Stochastic Container Relocation Problem

The Container Relocation Problem (CRP) is concerned with finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers, while respecting a given order of retrieval. However, the assumption of knowing the full retrieval order of containers is particularly unrealistic in real operations. This paper studies the stochastic CRP (SCRP), which relaxes this assumption. A new multi-stage stochastic model, called the batch model, is introduced, motivated, and compared with an existing model (the online model). The two main contributions are an optimal algorithm called Pruning-Best-First-Search (PBFS) and a randomized approximate algorithm called PBFS-Approximate with a bounded average error. Both algorithms, applicable in the batch and online models, are based on a new family of lower bounds for which we show some theoretical properties. Moreover, we introduce two new heuristics outperforming the best existing heuristics. Algorithms, bounds and heuristics are tested in an extensive computational section. Finally, based on strong computational evidence, we conjecture the optimality of the “Leveling” heuristic in a special “no information” case, where at any retrieval stage, any of the remaining containers is equally likely to be retrieved next

Selênio como suplemento para bovinos intoxicados cronicamente por Pteridium sp. no Espirito Santo. 2017.

Pteridiumsp.(samambaia) é uma planta responsável por diversos quadros de intoxicação em animais e seres humanos. Em bovinos, um dos quadros comuns na região sul do Espírito Santo é a hematúria enzoótica bovina (HEB) que não possui tratamento. Assim, o objetivo do presente trabalho foi determinar os efeitos do selênio associado a vitamina E como suplemento em animais intoxicados cronicamente pelo Pteridium sp. Foram selecionados 21 animais intoxicados cronicamente pela planta e com HEB. Os animais foram examinados clinicamente e foi realizada a coleta da urina para a confirmação da hematúria. O delineamento experimental foi feito em quatro grupos divididos ao acaso (controle soro fisiológico; tratamento 1 0,05 mg/Kg do suplemento;tratamento20,10mg/Kgdosuplemento;tratamento30,20mg/Kgdo suplemento). Foi feita a suplementação parenteral, via intramuscular, uma vez por semana, durante 13 semanas. Quinzenalmente os animais foram avaliados clinicamente e foram coletadas amostras de sangue para dosagem do selêniosérico. A análise de selênio foi feita nos momentos inicial, antes da suplementação com selênio (M0), após quatro semanas de tratamento (M4), após oito semanas (M8) e após 12 semanas (M12), pelo método de espectrofotometria de absorção atômica. Utilizou-seaanálisedevariância(ANOVA)seguidadotestedeTukeya5%.Verificou-se que houve maior ganho de peso dos animais tratados com selênio em relação ao grupocontrolee,também,entreosgrupos.Aintensidadedahematúriareduziuapartir da sexta semana e houve diferença significativa entre os grupos tratados e o grupo controle, assim como entre os grupos. Houve diferença significativa da concentração sérica de selênio entre os tratamentos. Assim, conclui-se que o selênio associado a vitaminaEcomosuplementoparabovinosintoxicadoscronicamenteporPteridiumsp. no Espirito Santo com quadro de HEB teve efeito dose dependente sobre a melhora doquadroclínicocausandoreduçãodaintensidadedehematúriaeaumentodoganho de pes

An average-case asymptotic analysis of the Container Relocation Problem

The Container Relocation Problem (CRP) involves finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers in a given order. In this paper, we focus on average case analysis of the CRP when the number of columns grows asymptotically. We show that the expected minimum number of relocations converges to a simple and intuitive lower-bound for which we give an analytical formula. Keywords: CRP; Asymptotic analysis; Expected lower boun