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Title: Graph Characterization and Sampling Algorithms.


Abstract not provided.

; ;  [1]
  1. (UC Santa Cruz)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
Report Number(s):
DOE Contract Number:
Resource Type:
Resource Relation:
Conference: Proposed for presentation at the Computer Information Science (CIS) Review held April 21-23, 2015 in Albuquerque, NM.
Country of Publication:
United States

Citation Formats

Kolda, Tamara G., Pinar, Ali, and Comandur, Seshadhri. Graph Characterization and Sampling Algorithms.. United States: N. p., 2015. Web.
Kolda, Tamara G., Pinar, Ali, & Comandur, Seshadhri. Graph Characterization and Sampling Algorithms.. United States.
Kolda, Tamara G., Pinar, Ali, and Comandur, Seshadhri. 2015. "Graph Characterization and Sampling Algorithms.". United States. doi:.
title = {Graph Characterization and Sampling Algorithms.},
author = {Kolda, Tamara G. and Pinar, Ali and Comandur, Seshadhri},
abstractNote = {Abstract not provided.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2015,
month = 4

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  • Abstract not provided.
  • Graph partitioning deals with evenly dividing a graph into two or more parts such that the total weight of edges interconnecting these parts, i.e., cutsize, is minimized. Graph partitioning has important applications in VLSI layout, mapping, and sparse Gaussian elimination. Since graph partitioning problem is NP-hard, we should resort to polynomial-time algorithms to obtain a good solution, or hopefully a near-optimal solution. Kernighan-Lin (KL) propsoed a 2-way partitioning algorithms. Fiduccia-Mattheyses (FM) introduced a faster version of KL algorithm. Sanchis (FMS) generalized FM algorithm to a multiple-way partitioning algorithm. Simulated Annealing (SA) is one of the most successful approaches that aremore » not KL-based.« less
  • We conduct an empirical study on some dynamic graph algorithms which where developed recently. The following implementations were tested and compared with simple algorithms: dynamic connectivity, and dynamic minimum 1 spanning tree based on sparsification by Eppstein et al.; dynamic connectivity based on a very recent paper by Henzinger and King. In our experiments, we considered both random and non-random inputs. Moreover, we present a simplified variant of the algorithm by Henzinger and King, which for random inputs was always faster than the original implementation. Indeed, this variant was among the fastest implementations for random inputs. For non-random inputs, sparsificationmore » was the fastest algorithm for small sequences of updates; for medium and large sequences of updates, the original algorithm by Henzinger and King was faster. Perhaps one of the main practical results of this paper is that our implementations of the sophisticated dynamic graph algorithms were faster than simpler algorithms for most practical values of the graph parameters, and competitive with simpler algorithms even in case of very small graphs (say graphs with less than a dozen vertices and edges). From the theoretical point of view, we analyze the average case running time of sparsification and prove that the logarithmic overhead for simple sparsification vanishes for dynamic random graphs.« less
  • We present the first randomized O(log n) time and O(m + n) work EREW PRAM algorithm for finding a spanning forest of an undirected graph G = (V, E) with n vertices and m edges. Our algorithm is optimal with respect to time, work and space. As a consequence we get optimal randomized EREW PRAM algorithms for other basic connectivity problems such as finding a bipartite partition, finding bridges and biconnected components, and finding Euler tours in Eulerean graphs. For other problems such as finding an ear decomposition, finding an open ear decomposition, finding a strong orientation, and finding anmore » st-numbering we get optimal randomized CREW PRAM algorithms.« less
  • Graph-based algorithms convert a knowledge base with a graph structure into one with a tree structure (a join-tree) and then apply tree-inference on the result. Nodes in the join-tree are cliques of variables and tree-inference is exponential in w*, the size of the maximal clique in the join-tree. A central property of join-trees that validates tree-inference is the running-intersection property: the intersection of any two cliques must belong to every clique on the path between them. We present two key results in connection to graph-based algorithms. First, we show that the running-intersection property, although sufficient, is not necessary for validatingmore » tree-inference. We present a weaker property for this purpose, called running-interaction, that depends on non-structural (semantical) properties of a knowledge base. We also present a linear algorithm that may reduce w* of a join-tree, possibly destroying its running-intersection property, while maintaining its running-interaction property and, hence, its validity for tree-inference. Second, we develop a simple algorithm for generating trees satisfying the running-interaction property. The algorithm bypasses triangulation (the standard technique for constructing join-trees) and does not construct a join-tree first. We show that the proposed algorithm may in some cases generate trees that are more efficient than those generated by modifying a join-tree.« less