We show that if a ow network has k input/output terminals (for the traditional maximum-ow problem , k = 2), its external ow pattern (possible values of ow at the terminals) has two characterizations of size independent of the total number of vertices: a set of at most 2 k inequalities in k variables representing ow values at the terminals, and a mimicking network with at most 2 2 k vertices and...

Nearest Neighbor (NN) searching is a challenging problem in data management and has been widely studied in data mining, pattern recognition and computational geometry. The goal of NN searching is efficiently reporting the nearest data to a given object as a query. In most of the studies both the data and query are assumed to be precise, however, due to the real applications of NN searching, suc...

In this paper, we study the MapReduce framework from an algorithmic standpoint and demonstrate the usefulness of our approach by designing and analyzing efficient MapReduce algorithms for fundamental sorting, searching, and simulation problems. This study is motivated by a goal of ultimately putting the MapReduce framework on an equal theoretical footing with the well-known PRAM and BSP paralle...

The star and pancake networks were recently proposed as attractive alternatives to the hypercube topology for interconnecting processors in a parallel computer. However, few parallel algorithms are known for these networks. In this paper, we present several data communication schemes and basic algorithms for these two networks. These algorithms are then used to develop parallel solutions to var...

We present a parallel algorithm for recognizing and representing a proper interval graph in O(log n) time with O(m + n) processors on the CREW PRAM, where m and n are the number of edges and vertices in the graph. The algorithm uses sorting to compute a weak linear ordering of the vertices, from which an interval representation is easily obtained. It is simple, uses no complex data structures, ...

Nakano et al. in [20] presented a timeand work-optimal algorithm for finding the smallest number of vertex-disjoint paths that cover the vertices of a cograph and left open the problem of applying their technique into other classes of graphs. Motivated by this issue we generalize their technique and apply it to the class of P4-sparse graphs, which forms a proper superclass of cographs. We show ...

A sequence d of integers is a degree sequence if there exists a (simple) graph G such that the components of d are equal to the degrees of the vertices of G. The graph G is said to be a realization of d. We provide an efficient parallel algorithm to realize d; the algorithm runs in O(logn) time using O(n+m) CRCW PRAM processors, where n and m are the number of vertices and edges in G. Before ou...

This paper proposes a novel technique to computing geometric information from images captured under parallel projections. Parallel images are desirable for stereo reconstruction because parallel projection significantly reduces foreshortening. As a result, correlation based matching becomes more effective. Since parallel projection cameras are not commonly available, we construct parallel image...

Calculations can naturally be described as graphs in which vertices represent computation and edges re ̄ect data dependencies. By partitioning the vertices of a graph, the calculation can be divided among processors of a parallel computer. However, the standard methodology for graph partitioning minimizes the wrong metric and lacks expressibility. We survey several recently proposed alternatives...

1 Elimination Game is a well known algorithm that simulates Gaussian elimination of matrices on graphs, and it computes a triangulation of the input graph. The number of fill edges in the computed triangulation is highly dependent on the order in which Elimination Game processes the vertices, and in general the produced triangulations are neither minimum nor minimal. In order to obtain a triang...