Adjacency list

About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.

A Parallel Graph Partitioning Algorithm for a Message-Passing Multiprocessor

Abstract: We develop a parallel algorithm for partitioning the vertices of a graph into $p \geq 2$ sets in such a way that few edges connect vertices in different sets The algorithm is intended for a message-passing multiprocessor system, such as the hypercube, and is based on the Kernighan-Lin algorithm for finding small edge separators on a single processor We use this parallel partitioning algorithm to find orderings for factoring large sparse symettric positive definite matrices These orderings not only reduce fill, but also result in good processor utilization and low communication overhead during the factorization We provide a complexity analysis of the algorithm, as well as some numerical results from an Intel hypercube and a hypercube simulator

Classification of web documents using graph matching

Abstract: In this paper we describe a classification method that allows the use of graph-based representations of data instead of traditional vector-based representations. We compare the vector approach combined with the k-Nearest Neighbor (k-NN) algorithm to the graph-matching approach when classifying three different web document collections, using the leave-one-out approach for measuring classification accuracy. We also compare the performance of different graph distance measures as well as various document representations that utilize graphs. The results show the graph-based approach can outperform traditional vector-based methods in terms of accuracy, dimensionality and execution time.

Better Algorithms for Counting Triangles in Data Streams

Abstract: We present space-efficient data stream algorithms for approximating the number of triangles in a graph up to a factor 1+e. While it can be shown that determining whether a graph is triangle-free is not possible in sub-linear space, a large body of work has focused on minimizing the space required in terms of the number of triangles T (or a lower bound on this quantity) and other parameters including the number of nodes n and the number of edges m. Two models are important in the literature: the arbitrary order model in which the stream consists of the edges of the graph in arbitrary order and the adjacency list order model in which all edges incident to the same node appear consecutively. We improve over the state of the art results in both models. For the adjacency list order model, we show that ~O(e-2m/√T) space is sufficient in one pass and ~O(e-2m3/2/T) space is sufficient in two passes where the ~O(·) notation suppresses log factors. For the arbitrary order model, we show that ~O(e-2m/√T) space suffices given two passes and that ~O(e-2m3/2/T) space suffices given three passes and oracle access to the degrees. Finally, we show how to efficiently implement the "wedge sampling" approach to triangle estimation in the arbitrary order model. To do this, we develop the first algorithm for lp sampling such that multiple independent samples can be generated with O(polylog n) update time; this primitive is widely applicable and this result may be of independent interest.