Polynomial-Time Space-Optimal Silent Self-Stabilizing Minimum-Degree Spanning Tree Construction

Motivated by applications to sensor networks, as well as to many other areas, this paper studies the construction of minimum-degree spanning trees. We consider the classical node-register state model, with a weakly fair scheduler, and we present a space-optimal \emph{silent} self-stabilizing construction of minimum-degree spanning trees in this model. Computing a spanning tree with minimum degree is NP-hard. Therefore, we actually focus on constructing a spanning tree whose degree is within one from the optimal. Our algorithm uses registers on $O(\log n)$ bits, converges in a polynomial number of rounds, and performs polynomial-time computation at each node. Specifically, the algorithm constructs and stabilizes on a special class of spanning trees, with degree at most $OPT+1$. Indeed, we prove that, unless NP $=$ coNP, there are no proof-labeling schemes involving polynomial-time computation at each node for the whole family of spanning trees with degree at most $OPT+1$. Up to our knowledge, this is the first example of the design of a compact silent self-stabilizing algorithm constructing, and stabilizing on a subset of optimal solutions to a natural problem for which there are no time-efficient proof-labeling schemes. On our way to design our algorithm, we establish a set of independent results that may have interest on their own. In particular, we describe a new space-optimal silent self-stabilizing spanning tree construction, stabilizing on \emph{any} spanning tree, in $O(n)$ rounds, and using just \emph{one} additional bit compared to the size of the labels used to certify trees. We also design a silent loop-free self-stabilizing algorithm for transforming a tree into another tree. Last but not least, we provide a silent self-stabilizing algorithm for computing and certifying the labels of a NCA-labeling scheme

Compact Deterministic Self-Stabilizing Leader Election: The Exponential Advantage of Being Talkative

This paper focuses on compact deterministic self-stabilizing solutions for the leader election problem. When the protocol is required to be \emph{silent} (i.e., when communication content remains fixed from some point in time during any execution), there exists a lower bound of Omega(\log n) bits of memory per node participating to the leader election (where n denotes the number of nodes in the system). This lower bound holds even in rings. We present a new deterministic (non-silent) self-stabilizing protocol for n-node rings that uses only O(\log\log n) memory bits per node, and stabilizes in O(n\log^2 n) rounds. Our protocol has several attractive features that make it suitable for practical purposes. First, the communication model fits with the model used by existing compilers for real networks. Second, the size of the ring (or any upper bound on this size) needs not to be known by any node. Third, the node identifiers can be of various sizes. Finally, no synchrony assumption, besides a weakly fair scheduler, is assumed. Therefore, our result shows that, perhaps surprisingly, trading silence for exponential improvement in term of memory space does not come at a high cost regarding stabilization time or minimal assumptions

Optimization of quality of charcoal for steelmaking using statistical analysis approach

Steel is one of the most important materials used in modern society. The majority of the steel produced today is based on the use of coke and contributes a lot to greenhouse gases emission. Many researchers have been laid on the possibility to replace part of the fossil-based energy source in iron making with renewable, biomass-derived reducing agent. The main problems of this replacement are some difference of in quality between coke and wood charcoal (more reactive, less strength and carbon content) It causes a little shutdown of production in blast furnace and additional cost to modify a furnace. The aim of this paper was to determine in a statistical manner how carbonizations parameters impact the charcoal quality, especially reactivity and mechanical parameter. We applied a random factorial design and used the General linear System procedure to perform the statistical analysis. The experimental study was carried out using Eucalyptus Urophylla and Eucalyptus Camadulensis wood and involved two carbonization temperature (350 and 600°C), two relative working pressure (2 and 6 bars) and two heating rates (1 and 5°C/min). Six response variables were analyzed and discussed following a random factorial design: the charcoal yield 61, j char), the fixed carbon content (C1), the bulk density (D), the compressive strength (Rm), friability (F) and the reactivity (R) of charcoal. Except for the friability of charcoal, all other property are well correlate with carbonization parameter. In the range of low carbonisation parameter, reactivity of charcoal is affected only by carbonization temperature. (Résumé d'auteur