111 research outputs found
A note on Pr\"ufer-like coding and counting forests of uniform hypertrees
This note presents an encoding and a decoding algorithms for a forest of
(labelled) rooted uniform hypertrees and hypercycles in linear time, by using
as few as integers in the range . It is a simple extension of
the classical Pr\"{u}fer code for (labelled) rooted trees to an encoding for
forests of (labelled) rooted uniform hypertrees and hypercycles, which allows
to count them up according to their number of vertices, hyperedges and
hypertrees. In passing, we also find Cayley's formula for the number of
(labelled) rooted trees as well as its generalisation to the number of
hypercycles found by Selivanov in the early 70's.Comment: Version 2; 8th International Conference on Computer Science and
Information Technologies (CSIT 2011), Erevan : Armenia (2011
Multiplicate inverse forms of terminating hypergeometric series
The multiplicate form of Gould--Hsu's inverse series relations enables to
investigate the dual relations of the Chu-Vandermonde-Gau{\ss}'s, the
Pfaff-Saalsch\"utz's summation theorems and the binomial convolution formula
due to Hagen and Rothe. Several identitity and reciprocal relations are thus
established for terminating hypergeometric series. By virtue of the duplicate
inversions, we establish several dual formulae of Chu-Vandermonde-Gau{\ss}'s
and Pfaff-Saalsch\"utz's summation theorems in Section (3)\cite{ChuVanGauss}
and (4)\cite{PfaffSaalsch}, respectively. Finally, the last section is devoted
to deriving several identities and reciprocal relations for terminating
balanced hypergeometric series from Hagen-Rothe's convolution identity in
accordance with the duplicate, triplicate and multiplicate inversions.Comment: 15 page
Overview of the Heisenberg--Weyl Algebra and Subsets of Riordan Subgroups
In a first part, we are concerned with the relationships between polynomials
in the two generators of the algebra of Heisenberg--Weyl, its Bargmann--Fock
representation with differential operators and the associated one-parameter
group.Upon this basis, the paper is then devoted to the groups of Riordan
matrices associated to the related transformations of matrices (i.e.
substitutions with prefunctions). Thereby, various properties are studied
arising in Riordan arrays, in the Riordan group and, more specifically, in the
`striped' Riordan subgroups; further, a striped quasigroup and a semigroup are
also examined. A few applications to combinatorial structures are also briefly
addressed in the Appendix.Comment: Version 3 of the paper entitled `On subsets of Riordan subgroups and
Heisenberg--Weyl algebra' in [hal-00974929v2]The present article is published
in The Electronic Journal of Combinatorics, Volume 22, Issue 4, 40 pages
(Oct. 2015), pp.Id: 1
Analysis of Link Reversal Routing Algorithms for Mobile Ad Hoc Networks
Link reversal (LR) algorithms provide a simple mechanisme for routing in communication networks whose topology is frequently changing, such as in mobile and ad hoc networks. A LR algorithm routes by imposing a direction on each network link such that the resulting graph is destination oriented (DAG). Whenever a node loses routes to the destination, is reacts by reversing some (or all) of its incident links. This survey presents the worst-case performance analysis of LR algorithms from the excellent work of Costas Busch and Srikanta Tirthapura (SIAM J. on Computing, 35(2):305- 326, 2005). The LR algorithms are studied in terms of work (number of node reversals) and time needed until the algorithm stabilizes to a state in which all the routes are reestablished. The full reversal algorithm and the partial reversal algorithm are considered. • The full reversal algorithm requires O(n2) work and time, where n is the number of nodes that have lost routes to the destination. This bound is tight in the worst case. • The partial reversal algorithm requires O(na*r + n2) work and time, where a*r is a non-negative integral function of the initial state of the network. Further, the partial reversal algorithm requires (na*r + n2) work and time. • There is an inherent lower bound on the worst-case performance of LR algorithms: \Omega(n2). Therefore, surprisingly, the full reversal algorithm is asymptotically optimal in the worst-case, while the partial reversal algorithm is not; since a*r can be arbitrarily larger than n
Exact average message complexity values for distributed election on bidirectional rings of processors
International audienceConsider a distributed system of n processors arranged on a ring. All processors are labeled with distinct identity-numbers, but are otherwise identical. In this paper, we make use of combinatorial enumeration methods in permutations and derive the one and the same exact asymptotic value, lJ2nH,,+O(n), of the expected number of messages in both probabilistic and deterministicbidirectional variants of Chang-Roberts distributed election algorithm. This confirms the result of Bodlaender and van Leeuwen (1986) that distributed Ieader finding is indeed strictly more efficient on bidirectional rings of processors than on unidirectional ones
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