Scaling large iterative graph processing applications through parallel computing is a very important problem. Several graph processing frameworks have been proposed that insulate developers from low-level details of parallel programming. Most of these frameworks are based on the bulk synchronous parallel (BSP) model in order to simplify application development. However, in the BSP model, vertic...

Graph Cut has proven to be an effective scheme to solve a wide variety of segmentation problems in graphics community. The main limitation of conventional graph-cut implementations is that they can hardly handle largescale datasets because of high computational complexity. Even though there are some parallelization solutions, they commonly suffer from the problems of low parallelism (on CPU) or...

For the task of moving a group of indistinguishable agents on a connected graph with unit edge lengths into an arbitrary goal formation, it was shown that distance optimal paths can be scheduled to complete with a tight convergence time guarantee [22], using a fully centralized algorithm. In this study, we show that the problem formulation in fact induces a more fundamental ordering of the vert...

In this paper we present a randomized parallel algorithm to sample matchings from an almost uniform distribution on the set of matchings of all sizes in a graph. First we prove that the direct NC simulation of the sequential Markov chain technique for this problem is P-complete. Afterwards we present a randomized parallel algorithm for the problem. The technique used is based on the definition ...

This paper proposes a new finite-time consensus tracking protocol for reaching the fast finite-time consensus tracking. The Lyapunov function method, algebra graph theory, and homogeneity with dilation are employed to obtain the convergence criteria. Numerical simulations show that compared with the traditional finite-time consensus tracking protocols, the proposed protocol can accelerate the c...

We study a model of mass redistribution on a finite graph. We address the questions of convergence to equilibrium and the rate of convergence. We present theorems on the distribution of empty sites and the distribution of mass at a fixed vertex. These distributions are related to random permutations with certain peak sets.

A p-star is a complete bipartite graph K1,p with one center node and p leaf nodes. In this paper we propose the first distributed self-stabilizing algorithm for graph decomposition into p-stars. For a graph G and an integer p ≥ 1, this decomposition provides disjoint components of G where each component forms a p-star. We prove convergence and correctness of the algorithm under an unfair distri...

Consider n points (or nodes) distributed uniformly and independently on the unit interval [0, 1]. Two nodes are said to be adjacent if their distance is less than some given threshold value. For the underlying random graph we derive zero-one laws for the property of graph connectivity and give the asymptotics of the transition widths for the associated phase transition. These results all flow f...

A key tool to analyze signals defined over a graph is the so called Graph Fourier Transform (GFT). Alternative definitions of GFT have been proposed, based on the eigendecomposition of either the graph Laplacian or adjacency matrix. In this paper, we introduce an alternative approach, valid for the general case of directed graphs, that builds the graph Fourier basis as the set of orthonormal ve...

In the outerplanar (other alternate concepts are circular or one-page) drawing, one places vertices of a n−vertex m−edge connected graph G along a circle, and the edges are drawn as straight lines. The minimal number of crossings over all outerplanar drawings of the graph G is called the outerplanar (circular, convex, or one-page) crossing number of the graph G. To find a drawing achieving the ...