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Some Optimal Parallel Algorithms on Interval and Circulararc Graphs *
"... In this paper, we consider some shortest path related problems on interval and circulararc graphs. For the allpair shortest path query problem on interval and circulararc graphs, instead of using the sophisticated technique, we propose simple parallel algorithms using only the parallel prefix and ..."
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In this paper, we consider some shortest path related problems on interval and circulararc graphs. For the allpair shortest path query problem on interval and circulararc graphs, instead of using the sophisticated technique, we propose simple parallel algorithms using only the parallel prefix
Optimal Distance Labeling for Interval and Circulararc Graphs
, 2003
"... In this paper we design a distance labeling scheme with O(log n) bit labels for interval graphs and circulararc graphs with n vertices. The set of all the labels is constructible in O(n) time if the interval representation of the graph is given and sorted. As a byproduct we give a new and simpl ..."
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Cited by 2 (0 self)
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and simpler O(n) space datastructure computable after O(n) preprocessing time, and supporting constant worstcase time distance queries for interval and circulararc graphs. These optimal bounds improve the previous scheme of Katz, Katz, and Peleg (STACS '00) by a log n factor. To the best of our
Some Optimal Parallel Algorithms for Shortest Path Related Problems on Interval and Circulararc Graphs
 PROC. OF THE 19TH WORKSHOP ON COMBINATORIAL MATHEMATICS AND COMPUTATION THEORY
"... In this paper, we consider some shortest path related problems on interval and circulararc graphs. For the allpair shortest path query problem on interval and circulararc graphs, instead of using the sophisticated technique, we propose simple parallel algorithms using only the parallel prefix and ..."
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In this paper, we consider some shortest path related problems on interval and circulararc graphs. For the allpair shortest path query problem on interval and circulararc graphs, instead of using the sophisticated technique, we propose simple parallel algorithms using only the parallel prefix
Minimum Fillin on Circle and CircularArc Graphs
 J. ALGORITHMS
, 1996
"... We present two algorithms solving the minimum fillin problem on circle graphs and on circulararc graphs in time O(n³). ..."
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Cited by 10 (0 self)
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We present two algorithms solving the minimum fillin problem on circle graphs and on circulararc graphs in time O(n³).
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
Interval Routing Schemes for CircularArc Graphs
, 2012
"... Interval routing is a space efficient method to realize a distributed routing function. In this paper, we show that every circulararc graph allows a shortest path strict 2interval routing scheme, i.e., a routing function that only implies shortest paths can be realized in every circulararc graph, ..."
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that the constructed 2interval routing scheme can be represented as an 1interval routing scheme with at most one additional interval assigned for each vertex of the graph and we outline an algorithm to implement the routing scheme for nvertex circulararc graphs in O(n2) time.
Parallel Algorithms for Connected Domination Problem on Interval and Circulararc Graphs
"... Abstract: A connected domination set of a graph is a set of vertices such that every vertex not in is adjacent to and the induced subgraph of is connected. The minimum connected domination set of a graph is the connected domination set with the minimum number of vertices. In this paper, we propo ..."
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propose parallel algorithms for finding the minimum connected domination set of interval graphs and circulararc graphs. Our algorithms run in time algorithm using processors while the intervals and arcs are given in sorted order. Our algorithms are on the EREW PRAM model.
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
Efficient Algorithms for the Domination Problems on Interval and CircularArc Graphs
 SIAM J. Comput
, 1998
"... Abstract. This paper first presents a unified approach to design efficient algorithms for the weighted domination problem and its three variants, i.e., the weighted independent, connected, and total domination problems, on interval graphs. Given an interval model with endpoints sorted, these algorit ..."
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Cited by 14 (1 self)
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, these algorithms run in time O(n) orO(n log log n) where n is the number of vertices. The results are then extended to solve the same problems on circulararc graphs in O(n + m) time where m is the number of edges of the input graph.
On the Cubicity of ATfree graphs and Circulararc graphs
, 2008
"... A unit cube in k dimensions (kcube) is defined as the the Cartesian product R1 × R2 × · · · × Rk where Ri(for 1 ≤ i ≤ k) is a closed interval of the form [ai, ai + 1] on the real line. A graph G on n nodes is said to be representable as the intersection of kcubes (cube representation in k dim ..."
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free graphs, circulararc graphs and cocomparability graphs which have O(∆) bandwidth. Thus we have: 1. cub(G) ≤ 3 ∆ − 1, if G is an ATfree graph. 2. cub(G) ≤ 2 ∆ + 1, if G is a circulararc graph. 3. cub(G) ≤ 2∆, if G is a cocomparability graph. Also for these graph classes, there are constant factor
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