A number of priors have been recently developed for Bayesian estimation of sparse models. In many applications the variables are simultaneously relevant or irrelevant in groups, and appropriately modeling this correlation is important for improved sample efficiency. Although group sparse priors are also available, most of them are either limited to disjoint groups, or do not infer sparsity at g...

We present the first constant-factor approximation algorithm for a non-trivial instance of the optimal guarding (coverage) problem in polygons. In particular, we give an O(1)-approximation algorithm for placing the fewest point guards on a 1.5D terrain, so that every point of the terrain is seen by at least one guard. While polylogarithmic-factor approximations follow from set cover results, ou...

This paper presents a software platform for the distributed solution of complex optimization problems. For such problems there are often no outstanding approaches which always perform well. That is why we propose to use diierent solution methods simultaneously. They can communicate and thus prootate from each other. Some general paradigms are applicable to a wide class of problems. Our platform...

Given an undirected graph, a bramble is a set of connected subgraphs (called bramble elements) such that every pair of subgraphs either contains a common node, or such that an edge (i, j) exists with node i belonging to one subgraph and node j belonging to the other. In this paper, we examine the problem of finding the bramble number of a graph, along with a set of bramble elements that yields ...

The condition of t-resilience stipulates that an n-process program is only obliged to make progress when at least n− t processes are correct. Put another way, the live sets, the collection of process sets such that progress is required if all the processes in one of these sets are correct, are all sets with at least n − t processes. In this paper we study what happens when the live sets are any...

We give a general framework for the problem of finding all minimal hitting sets of a family of objects in R by another. We apply this framework to the following problems: (i) hitting hyper-rectangles by points in R; (ii) stabbing connected objects by axis-parallel hyperplanes in R; and (iii) hitting half-planes by points. For both the covering and hitting set versions, we obtain incremental pol...

We will consider set–covering models for diagnostic tasks handling uncertain knowledge. Because these models have to be build manually by domain experts, we will show how this effort can be reduced by an incremental development of the set–covering models. Thus simple models can be enhanced by similarities, weights and uncertainty to increase the quality of the knowledge and the resulting system...

A hypergraph F is a set family defined on vertex set V . The dual of F is the set of minimal subsetsH of V such that F∩H 6= ∅ for any F ∈ F . The computation of the dual is equivalent to many problems, such as minimal hitting set enumeration of a subset family, minimal set cover enumeration, and the enumeration of hypergraph transversals. Although many algorithms have been proposed for solving ...

We present an inductive learning algorithm that allows for a partial completeness and consistence, i.e. that derives classification rules correctly describing, e.g, most of the examples belonging to a class and not describing most of the examples not belonging to this class. The problem is represented as a modification of the set covering problem that is solved by a greedy algorithm. The approa...

One of the best examples of combinatorial approximation algorithms is a greedy algorithm approximating the (weighted) SET COVER problem. An instance of the SET COVER problem consists of a universe set U = {1, . . . ,m}, a family S = {S1, . . . , Sn} of subsets of U , where set S ∈ S is weighted with wS . We want to find a sub-family of S with minimum total weight such that the union of the sub-...