In this paper we study the problem of computing approximate vertex covers of a graph on the basis of partial information in the distributed decision-making model proposed by Deng and Papadimitriou 1]. In particular, we show an optimal algorithm whose competitive ratio is equal to p, where p is the number of processors.

Studies on ensemble methods for classification suffer from the difficulty of modeling the complementary strengths of the components. Kleinberg’s theory of stochastic discrimination (SD) addresses this rigorously via mathematical notions of enrichment, uniformity, and projectability of a model ensemble. We explain these concepts via a very simple numerical example that captures the basic princip...

The task of identifying redundant information in documents that are generated from multiple sources provides a significant challenge for summarization and QA systems. Traditional clustering techniques detect redundancy at the sentential level and do not guarantee the preservation of all information within the document. We discuss an algorithm that generates a novel graph-based representation fo...

The 3-Hitting Set problem involves a family of subsets F of size at most three over an universe U . The goal is to find a subset of U of the smallest possible size that intersects every set in F . The version of the problem with parity constraints asks for a subset S of size at most k that, in addition to being a hitting set, also satisfies certain parity constraints on the sizes of the interse...

We develop a dynamic version of the primal-dual method for optimization problems, and apply it to obtain the following results. (1) For the dynamic set-cover problem, we maintain an O(f)approximately optimal solution in O(f · log(m + n)) amortized update time, where f is the maximum “frequency” of an element, n is the number of sets, andm is the maximum number of elements in the universe at any...

We propose a novel hierarchical clustering algorithm for data-sets in which only pairwise distances between the points are provided. The classical Hungarian method is an efficient algorithm for solving the problem of minimal-weight cycle cover. We utilize the Hungarian method as the basic building block of our clustering algorithm. The disjoint cycles, produced by the Hungarian method, are view...

Some rigorous results and statistics of the solution space of Vertex-Covers on bipartite graphs are given in this paper. Based on the König’s theorem, an exact solution space expression algorithm is proposed and statistical analysis of the nodes’ states is provided. The statistical results fit well with the algorithmic results until the emergence of the unfrozen core, which makes the fluctuatio...

k-means is a widely used clustering algorithm, but for k clusters and a dataset size of N , each iteration of Lloyd’s algorithm costs O(kN) time. Although there are existing techniques to accelerate single Lloyd iterations, none of these are tailored to the case of large k, which is increasingly common as dataset sizes grow. We propose a dual-tree algorithm that gives the exact same results as ...

Nonperturbative effects in c < 1 noncritical string theory are studied using the two-matrix model. Such effects are known to have the form fixed by the string equations but the numerical coefficients have not been known so far. Using the method proposed recently, we show that it is possible to determine the coefficients for (p, q) string theory. We find that they are indeed finite in the double...

BACKGROUND Linking animal movements to landscape features is critical to identify factors that shape the spatial behaviour of animals. Habitat selection is led by behavioural decisions and is shaped by the environment, therefore the landscape is crucial for the analysis. Land cover classification based on ground survey and remote sensing data sets are an established approach to define landscape...