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Fast Approximation of Centrality
 Journal of Graph Algorithms and Applications
, 2001
"... Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized approximation algorithm for centrality in weighted graphs. For g ..."
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Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized approximation algorithm for centrality in weighted graphs. For graphs exhibiting the small world phenomenon, our method estimates the centrality of all vertices with high probability within a (1 + #) factor in nearlinear time. 1 Introduction In social network analysis, the vertices of a graph represent agents in a group and the edges represent relationships, such as communication or friendship. The idea of applying graph theory to analyze the connection between the structural centrality and group process was introduced by Bavelas [4]. Various measurement of centrality [7, 14, 15] have been proposed for analyzing communication activity, control, or independence within a social network. We are particularly interested in closeness centrality [5, 6, 24]...
An optimal algorithm for shortest paths on weighted interval and circulararc graphs, with applications, Algorithmica 14
, 1995
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Solving the AllPair Shortest Path Query Problem on Interval and CircularArc Graphs
 Networks
, 1998
"... In this paper, we study the following allpair shortest path query problem: Given the interval model of an unweighted interval graph of n vertices, build a data structure such that each query on the shortest path (or its length) between any pair of vertices of the graph can be processed efficiently ..."
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In this paper, we study the following allpair shortest path query problem: Given the interval model of an unweighted interval graph of n vertices, build a data structure such that each query on the shortest path (or its length) between any pair of vertices of the graph can be processed efficiently (both sequentially and in parallel). We show that, after sorting the input intervals by their endpoints, a data structure can be constructed sequentially in O(n) time and O(n) space; using this data structure, each query on the length of the shortest path between any two intervals can be answered in O(1) time, and each query on the actual shortest path can be answered in O(k) time, where k is the number of intervals on that path. Furthermore, this data structure can be constructed optimally in parallel, in O(log n) time using O(n= log n) CREW PRAM processors; each query on the actual shortest path can be answered in O(1) time using k processors. Our techniques can be extended to solving the ...
Solving the AllPairsShortestLength Problem on Chordal Bipartite Graphs
"... The allpairsshortestlength (APSL) problem of a graph is to find the lengths of the shortest paths between all pairs of vertices. In this paper, we study the APSL problem on chordal bipartite graphs. By a simple reduction, we show that solving the APSL problem on chordal bipartite graphs can be tr ..."
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The allpairsshortestlength (APSL) problem of a graph is to find the lengths of the shortest paths between all pairs of vertices. In this paper, we study the APSL problem on chordal bipartite graphs. By a simple reduction, we show that solving the APSL problem on chordal bipartite graphs can be transformed to solving the same problem on certain strongly chordal graphs. Consequently, there is an O(n 2 ) timeoptimal algorithm for this problem. Keywords: shortest paths, chordal bipartite graphs, strongly chordal graphs. All correspondence should be addressed to Professor ChinWen Ho, Institute of Computer Science and Information Engineering, National Central University, ChungLi, Taiwan 32054. (email: hocw@csie.ncu.edu.tw) 1 . Introduction All graphs considered in this paper are undirected, loopless and without multiple edges. Let G = (V; E) be a graph with vertex set V of size n and edge set E of size m. If G is associated with a weighted function w : E ! R, the length of a pa...
AN OPTIMAL PARALLEL ALGORITHM FOR SOLVING ALLPAIRS SHORTEST PATHS PROBLEM ON CIRCULARARC GRAPHS
"... Abstract. The shortestpaths problem is a fundamental problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematicall ..."
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Abstract. The shortestpaths problem is a fundamental problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The shortestpath between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one vertex to another often gives the best way to route a message between the vertices. This paper presents an O(n2) time sequential algorithm and an O(n2/p + log n) time parallel algorithm on EREW PRAM model for solving all pairs shortest paths problem on circulararc graphs, where p and n represent respectively the number of processors and the number of vertices of the circulararc graph.
Computation of Average Distance, Radius and Centre of a CircularArc Graph in Parallel
, 2006
"... The determination of centre of a graph is very important task in facility location problem. Computation of centre depends on the computation of radius of the graph. In this paper, we have design some parallel algorithms to find the average distance, radius, diameter and centre of a circulararc grap ..."
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The determination of centre of a graph is very important task in facility location problem. Computation of centre depends on the computation of radius of the graph. In this paper, we have design some parallel algorithms to find the average distance, radius, diameter and centre of a circulararc graph. The proposed parallel algorithms run in O(n 2 /p + log n) time on a EREW PRAM, where p and n represent respectively the number of processors and the number of vertices of the circulararc graph.
Annals of Some Algorithms on Cactus Graphs
, 2012
"... Abstract. A cactus graph is a connected graph in which every block is either an edge or a cycle. In this paper we give a brief idea how to design some optimal algorithms on cactus graphs in O(n) time, where n is the total number of vertices of the graph. The cactus graph has many applications in rea ..."
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Abstract. A cactus graph is a connected graph in which every block is either an edge or a cycle. In this paper we give a brief idea how to design some optimal algorithms on cactus graphs in O(n) time, where n is the total number of vertices of the graph. The cactus graph has many applications in real life problems, specially in radio communication system.