Cycles in the burnt pancake graphs

The pancake graph $P_n$ is the Cayley graph of the symmetric group $S_n$ on $n$ elements generated by prefix reversals. $P_n$ has been shown to have properties that makes it a useful network scheme for parallel processors. For example, it is $(n-1)$-regular, vertex-transitive, and one can embed cycles in it of length $\ell$ with $6\leq\ell\leq n!$. The burnt pancake graph $BP_n$, which is the Cayley graph of the group of signed permutations $B_n$ using prefix reversals as generators, has similar properties. Indeed, $BP_n$ is $n$-regular and vertex-transitive. In this paper, we show that $BP_n$ has every cycle of length $\ell$ with $8\leq\ell\leq 2^n n!$. The proof given is a constructive one that utilizes the recursive structure of $BP_n$. We also present a complete characterization of all the $8$-cycles in $BP_n$ for $n \geq 2$, which are the smallest cycles embeddable in $BP_n$, by presenting their canonical forms as products of the prefix reversal generators.Comment: Added a reference, clarified some definitions, fixed some typos. 42 pages, 9 figures, 20 pages of appendice

On one-way cellular automata with a fixed number of cells

We investigate a restricted one-way cellular automaton (OCA) model where the number of cells is bounded by a constant number k, so-called kC-OCAs. In contrast to the general model, the generative capacity of the restricted model is reduced to the set of regular languages. A kC-OCA can be algorithmically converted to a deterministic finite automaton (DFA). The blow-up in the number of states is bounded by a polynomial of degree k. We can exhibit a family of unary languages which shows that this upper bound is tight in order of magnitude. We then study upper and lower bounds for the trade-off when converting DFAs to kC-OCAs. We show that there are regular languages where the use of kC-OCAs cannot reduce the number of states when compared to DFAs. We then investigate trade-offs between kC-OCAs with different numbers of cells and finally treat the problem of minimizing a given kC-OCA

Efficient Implementation of a Synchronous Parallel Push-Relabel Algorithm

Motivated by the observation that FIFO-based push-relabel algorithms are able to outperform highest label-based variants on modern, large maximum flow problem instances, we introduce an efficient implementation of the algorithm that uses coarse-grained parallelism to avoid the problems of existing parallel approaches. We demonstrate good relative and absolute speedups of our algorithm on a set of large graph instances taken from real-world applications. On a modern 40-core machine, our parallel implementation outperforms existing sequential implementations by up to a factor of 12 and other parallel implementations by factors of up to 3

The essence of P2P: A reference architecture for overlay networks

The success of the P2P idea has created a huge diversity of approaches, among which overlay networks, for example, Gnutella, Kazaa, Chord, Pastry, Tapestry, P-Grid, or DKS, have received specific attention from both developers and researchers. A wide variety of algorithms, data structures, and architectures have been proposed. The terminologies and abstractions used, however, have become quite inconsistent since the P2P paradigm has attracted people from many different communities, e.g., networking, databases, distributed systems, graph theory, complexity theory, biology, etc. In this paper we propose a reference model for overlay networks which is capable of modeling different approaches in this domain in a generic manner. It is intended to allow researchers and users to assess the properties of concrete systems, to establish a common vocabulary for scientific discussion, to facilitate the qualitative comparison of the systems, and to serve as the basis for defining a standardized API to make overlay networks interoperable

Life of occam-Pi

This paper considers some questions prompted by a brief review of the history of computing. Why is programming so hard? Why is concurrency considered an “advanced” subject? What’s the matter with Objects? Where did all the Maths go? In searching for answers, the paper looks at some concerns over fundamental ideas within object orientation (as represented by modern programming languages), before focussing on the concurrency model of communicating processes and its particular expression in the occam family of languages. In that focus, it looks at the history of occam, its underlying philosophy (Ockham’s Razor), its semantic foundation on Hoare’s CSP, its principles of process oriented design and its development over almost three decades into occam-? (which blends in the concurrency dynamics of Milner’s ?-calculus). Also presented will be an urgent need for rationalisation – occam-? is an experiment that has demonstrated significant results, but now needs time to be spent on careful review and implementing the conclusions of that review. Finally, the future is considered. In particular, is there a future