Topic
K-tree
About: K-tree is a research topic. Over the lifetime, 427 publications have been published within this topic receiving 12096 citations.
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TL;DR: Both the sequential and parallel algorithms use a concept introduced in this paper called the kernel of a k -tree, a subclass of the class of chordal graphs, for the fast reordering problem and the isomorphism problem.
Abstract: In this paper two problems on the class of k -trees, a subclass of the class of chordal graphs, are considered: the fast reordering problem and the isomorphism problem. An O(log 2n) time parallel algorithm for the fast reordering problem is described that uses O(nk(n-k)/\kern -1ptlog n) processors on a CRCW PRAM proving membership in the class NC for fixed k . An O(nk(k+1)!) time sequential algorithm for the isomorphism problem is obtained representing an improvement over the O(n2k(k+1)!) algorithm of Sekharan (the second author) [10]. A parallel version of this sequential algorithm is presented that runs in O(log 2n) time using O((nk((k+1)!+n-k))/log n) processors improving on a parallel algorithm of Sekharan for the isomorphism problem [10]. Both the sequential and parallel algorithms use a concept introduced in this paper called the kernel of a k -tree.
11 citations
TL;DR: It is shown that diam(Kn(G)) = diam(G) — n if G is a connected chordal graph and n ≤ diam( G) and this generalizes a similar result for time graphs by Bruce Hedman.
Abstract: The clique graph K(G) of a graph is the intersection graph of maximal cliques of G. The iterated clique graph Kn(G) is inductively defined as K(Kn−1(G)) and K1(G) = K(G). Let the diameter diam(G) be the greatest distance between all pairs of vertices of G. We show that diam(Kn(G)) = diam(G) — n if G is a connected chordal graph and n ≤ diam(G). This generalizes a similar result for time graphs by Bruce Hedman.
10 citations
TL;DR: This paper proposes a linear time algorithm, CM-Constructor (Candidate Map Constructor), for maximal clique enumeration in large sparse graphs which generates a novel data structure called candidate map as result.
10 citations
TL;DR: In this paper, a more efficient greedy algorithm for chordal graph partitioning is presented, which eliminates a subset of the leaf cliques % of the current graph at each step, and an algorithm implementing the scheme in time and space linear in the size of the clique tree is provided.
10 citations
TL;DR: It is shown that a known necessary condition for a graph to be an edge clique graph is that the sizes of all maximal cliques and intersections of maximal clique ought to be triangular numbers, and that this condition is also sufficient for starlike-threshold graphs.
10 citations