Jair Donadelli

Searching in random partially ordered sets

We consider the problem of searching for a given element in a partially ordered set. More precisely, we address the problem of computing efficiently near-optimal search strategies for typical partial orders under two classical models for random partial orders, the random graph model and the uniform model.We shall show that the problem of determining an optimal strategy is NP-hard, but there are simple, fast algorithms able to produce near-optimal search strategies for typical partial orders under the two models of random partial orders that we consider. We present a (1 + o(1))- approximation algorithm for typical partial orders under the random graph model (constant p) and present a 6.34-approximation algorithm for typical partial orders under the uniform model. Both algorithms run in polynomial time.

Ramsey minimal graphs

As usual, for graphs G, G, and H, we write G ® (G, H) to mean that any red-blue colouring of the edges of G contains a red copy of G or a blue copy of H. A pair of graphs (G, H) is said to be Ramsey-infinite if there are infinitely many minimal graphs F for which we have G ® (G, H). Let l > 4 be an integer. We show that if H is a 2-connected graph that does not contain induced cycles of length at least l, then the pair (Ck,H) is Ramsey-infinite for any k > l, where Ck denotes the cycle of length k.

Searching in Random Partially Ordered Sets

We consider the problem of searching for a given element in a partially ordered set. More precisely, we address the problem of computing efficiently near-optimal search strategies for typical partial orders. We consider two classical models for random partial orders, the random graph model and the uniform model.We shall show that certain simple, fast algorithms are able to produce nearly-optimal search strategies for typical partial orders under the two models of random partial orders that we consider. For instance, our algorithm for the random graph model produces, in linear time, a search strategy that makes O((log n)1/2 log log n) more queries than the optimal strategy, for almost all partial orders on n elements. Since we need to make at least lg n = log2 n queries for any n-element partial order, our result tells us that one may efficiently devise near-optimal search strategies for almost all partial orders in this model (the problem of determining an optimal strategy is NP-hard, as proved recently in [1]).

Engenharia reversa em Jogos de Minoria

Neste trabalho estamos interessados em descobrir as estrategias utilizadas por um conjunto de investidores que sao recompensados por comprar quando a maioria esta vendendo e por vender quando a maioria esta comprando (lei da oferta e procura). As decisoes de cada jogador sao descrita por matrizes de estrategias num Jogo de Minoria. Chamamos de engenharia reversa o conjunto de procedimentos que permitem conhecer estas matrizes a partir do valor agregado das decisoes individuais. Para encontrar tais matrizes implementamos dois algoritmos, um com a tecnica conhecida por Algoritmos Geneticos e outro baseado em Programacao Linear Inteira Mista. Tambem, a partir das matrizes foi possivel selecionar os jogadores mais influentes. Infiltramos jogadores com essas estrategias mais influentes em um novo jogo e observamos resultados positivos em seus desempenhos.

Deterministic and efficient minimal perfect hashing schemes

Neste trabalho apresentamos versoes deterministicas para os esquemas de hashing de Botelho, Kohayakawa e Ziviani (2005) e por Botelho, Pagh e Ziviani (2007). Tambem respondemos a um problema deixado em aberto no primeiro dos trabalhos, relacionado a prova da corretude e a analise de complexidade do esquema por eles proposto. As versoes deterministicas desenvolvidas foram implementadas e testadas sobre conjuntos de dados com ate 25.000.000 de chaves, e os resultados verificados se mostraram equivalentes aos dos algoritmos aleatorizados originais.