Recognizing Recursive
نویسنده
چکیده
Recursive circulant graphs G(N; d) have been introduced in 1994 by Park and Chwa [PC94] as a new topology for interconnection networks. Recursive circulant graphs G(N; d) are circulant graphs with N nodes and with jumps of powers of d. A subfamily of recursive circulant graphs (more precisely, G(2; 4)) is of same order and degree than the hypercube of dimension k, with sometimes better parameters, such as diameter [PC94,GMR98]. Embeddings among recursive circulant graphs, hypercubes and Kn odel graphs of order 2 have also been studied in [PC,FR98b]. Here, following a question raised in [CFG99], we give, thanks to a sharp structural analysis of such graphs, an O(cd (2m)) algorithm to determine if a given graph is a recursive circulant graph of the form G(cd; d), for any d 3, except in the case where c is even while d is odd. Notably, in the case where d = O(1), this gives an O(N (log(N))) algorithm, with N = cd. Moreover, applying this algorithm to recursive circulant graphs G(2; 4) gives us an O(2 k) recognition algorithm for such graphs.
منابع مشابه
Recognizing Recursive Circulant Graphs G(cd M ; D)
Recursive circulant graphs G(N; d) have been introduced in 1994 by Park and Chwa PC94] as a new topology for interconnection networks. Recursive circulant graphs G(N; d) are circu-lant graphs with N nodes and with jumps of powers of d. A subfamily of recursive circulant graphs (more precisely, G(2 k ; 4)) is of same order and degree than the hypercube of dimension k, with sometimes better param...
متن کاملThe eccentric connectivity index of bucket recursive trees
If $G$ is a connected graph with vertex set $V$, then the eccentric connectivity index of $G$, $xi^c(G)$, is defined as $sum_{vin V(G)}deg(v)ecc(v)$ where $deg(v)$ is the degree of a vertex $v$ and $ecc(v)$ is its eccentricity. In this paper we show some convergence in probability and an asymptotic normality based on this index in random bucket recursive trees.
متن کاملLimit distribution of the degrees in scaled attachment random recursive trees
We study the limiting distribution of the degree of a given node in a scaled attachment random recursive tree, a generalized random recursive tree, which is introduced by Devroye et. al (2011). In a scaled attachment random recursive tree, every node $i$ is attached to the node labeled $lfloor iX_i floor$ where $X_0$, $ldots$ , $X_n$ is a sequence of i.i.d. random variables, with support in [0,...
متن کاملBranches in random recursive k-ary trees
In this paper, using generalized {polya} urn models we find the expected value of the size of a branch in recursive $k$-ary trees. We also find the expectation of the number of nodes of a given outdegree in a branch of such trees.
متن کاملCursive Handwriting Segmentation Using Ideal Distance Approach
Received Jan 11, 2017 Revised Apr 7, 2017 Accepted Jun 11, 2017 Offline cursive handwriting becomes a major challenge due to the huge amount of handwriting varieties such as slant handwriting, space between words, the size and direction of the letter, the style of writing the letter and handwriting with contour similarity on some letters. There are some steps for recursive handwriting recogniti...
متن کامل