We consider a set of S independent encoders that must transmit a set of correlated sources through a network of noisy, independent, broadcast channels to T receivers, with no interference at the receivers. For the general problem of sending correlated sources through broadcast networks, it is known that the source–channel separation theorem breaks down and the achievable rate region as well as ...

We introduce the concept of randomized sparsiication of a weighted, undirected graph. Randomized sparsi-cation yields a sparse unweighted graph which closely approximates the minimum cut structure of the original graph. As a consequence, we show that a cut of weight within a (1 +) multiplicative factor of the minimum cut in a graph can be found in O(m + n(log 3 n)== 4) time; thus any constant f...

For a static array A of n totally ordered objects, a range minimum query asks for the position of the minimum between two specified array indices. We show how to preprocess A into a scheme of size 2n + o(n) bits that allows to answer range minimum queries on A in constant time. This space is asymptotically optimal in the important setting where access to A is not permitted after the preprocessi...

We are motivated by an application to extract a representative subset of machine learning training data and by the poor empirical performance we observe of the popular minimum norm algorithm. In fact, for our application, minimum norm can have a running time of about O(n) (O(n) oracle calls). We therefore propose a fast approximate method to minimize arbitrary submodular functions. For a large ...

In this paper we present algorithms that compute large matchings in planar graphs with fixed minimum degree. The algorithms give a guarantee on the size of the computed matching and run in linear time. Thus they are faster than the best known algorithm for computing maximum matchings in general graphs and in planar graphs, which run in O( √ nm) and O(n) time, respectively. For the class of plan...

Given a graph G, we give a fast algorithm for approximating the vertex connectivity κ of G. Our algorithm delivers a minimum vertex cut of G if κ <= δ/2 , and returns a message “κ > δ/2 ” otherwise, where δ denotes the minimum degree of G. The algorithm runs in O(n2(1+min{κ2, κ√n}/δ)) time and O(n+m) space, where n and m denote the numbers of vertices and edges in G, respectively. key words: gr...

We are motivated by an application to extract a representative subset of machine learning training data and by the poor empirical performance we observe of the popular minimum norm algorithm. In fact, for our application, minimum norm can have a running time of about O(n) (O(n) oracle calls). We therefore propose a fast approximate method to minimize arbitrary submodular functions. For a large ...

We design an O(m) algorithm to find a minimum weighted colouring and a maximum weighted clique of a perfectly ordered graph. We also present two O(n’) algorithms to find a minimum weighted colouring of a comparability graph and of a triangulated graph. Our colouring algorithms use an algorithm to find a stable set meeting all maximal (with respect to set inclusion) cliques of a perfectly ordere...