Self-Stabilizing Distributed Algorithms by Gellular Automata

2021 ◽  
Vol 30 (2) ◽  
pp. 159-185
Author(s):  
Taiga Hongu ◽  
◽  
Masami Hagiya ◽  
Keyword(s):  
Distributed Computing ◽  
Cellular Automata ◽  
Distributed Algorithms ◽  
Spanning Tree ◽  
Initial Configuration ◽  
Tree Construction

Gellular automata are cellular automata with the properties of asynchrony, Boolean totality and noncamouflage. In distributed computing, it is essential to determine whether problems can be solved by self-stable gellular automata. From any initial configuration, self-stable gellular automata converge to desired configurations, as self-stability implies the ability to recover from temporary malfunctions in transitions or states. This paper shows that three typical problems in distributed computing, namely, solving a maze, distance-2 coloring and spanning tree construction, can be solved with self-stable gellular automata.

scholarly journals Algorithms for the power-p Steiner tree problem in the Euclidean plane

2018 ◽  
Vol 25 (4) ◽  
pp. 28
Author(s):  
Christina Burt ◽  
Alysson Costa ◽  
Charl Ras
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Valid Inequalities ◽  
Minimum Cost ◽  
Performance Ratio ◽  
Mixed Integer ◽  
Steiner Tree Problem ◽  
Steiner Points ◽  
Tree Construction ◽  
The Cost

We study the problem of constructing minimum power-$p$ Euclidean $k$-Steiner trees in the plane. The problem is to find a tree of minimum cost spanning a set of given terminals where, as opposed to the minimum spanning tree problem, at most $k$ additional nodes (Steiner points) may be introduced anywhere in the plane. The cost of an edge is its length to the power of $p$ (where $p\geq 1$), and the cost of a network is the sum of all edge costs. We propose two heuristics: a ``beaded" minimum spanning tree heuristic; and a heuristic which alternates between minimum spanning tree construction and a local fixed topology minimisation procedure for locating the Steiner points. We show that the performance ratio $\kappa$ of the beaded-MST heuristic satisfies $\sqrt{3}^{p-1}(1+2^{1-p})\leq \kappa\leq 3(2^{p-1})$. We then provide two mixed-integer nonlinear programming formulations for the problem, and extend several important geometric properties into valid inequalities. Finally, we combine the valid inequalities with warm-starting and preprocessing to obtain computational improvements for the $p=2$ case.

scholarly journals Fast Self-stabilizing Minimum Spanning Tree Construction

2010 ◽  
pp. 480-494 ◽  
Author(s):  
Lélia Blin ◽  
Shlomi Dolev ◽  
Maria Gradinariu Potop-Butucaru ◽  
Stephane Rovedakis
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Tree Construction

Distributed Algorithms for Delay Bounded Minimum Energy Wireless Broadcasting

2010 ◽  
pp. 1677-1697
Author(s):  
Serkan Çiftlikli ◽  
Figen Öztoprak ◽  
Özgür Erçetin ◽  
Kerem Bülbül
Keyword(s):  
Distributed Algorithms ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Minimum Energy ◽  
Transmission Power ◽  
Message Complexity ◽  
Delay Constraint ◽  
Delay Bound ◽  
Lower Power ◽  
Tree Expansion

In this article, we investigate two different distributed algorithms for constructing a minimum power broadcast tree with a maximum depth ? which corresponds to the maximum tolerable end-to-end delay in the network. Distributed Tree Expansion (DTE) is based on an implementation of a distributed minimum spanning tree algorithm in which the tree grows at each iteration by adding a node that can cover the maximum number of currently uncovered nodes in the network with minimum incremental transmission power and without violating the delay constraint. In Distributed Link Substitution (DLS), given a feasible broadcast tree, the solution is improved by replacing expensive transmissions by transmissions at lower power levels while reserving the feasibility of the tree with respect to the delay bound. Although DTE increases the message complexity to O(n3) from O(n2?) in a network of size n, it provides up to 50% improvement in total expended power compared to DLS.

scholarly journals Random minimal directed spanning trees and Dickman-type distributions

2004 ◽  
Vol 36 (03) ◽  
pp. 691-714 ◽  
Author(s):  
Mathew D. Penrose ◽  
Andrew R. Wade
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Dirichlet Distribution ◽  
Maximal Length ◽  
Directed Path ◽  
Limiting Distributions ◽  
Limit Distributions ◽  
Tree Construction ◽  
Directed Spanning Tree ◽  
Westerly Direction

In Bhatt and Roy's minimal directed spanning tree construction fornrandom points in the unit square, all edges must be in a south-westerly direction and there must be a directed path from each vertex to the root placed at the origin. We identify the limiting distributions (for largen) for the total length of rooted edges, and also for the maximal length of all edges in the tree. These limit distributions have been seen previously in analysis of the Poisson-Dirichlet distribution and elsewhere; they are expressed in terms of Dickman's function, and their properties are discussed in some detail.

A declarative approach to distributed computing: Specification, execution and analysis

2013 ◽  
Vol 13 (4-5) ◽  
pp. 815-830 ◽  
Author(s):  
JIEFEI MA ◽  
FRANCK LE ◽  
DAVID WOOD ◽  
ALESSANDRA RUSSO ◽  
JORGE LOBO
Keyword(s):  
Distributed Computing ◽  
Distributed Algorithms ◽  
Answer Set Programming ◽  
Network Protocols ◽  
State Machines ◽  
Network Applications ◽  
Communication Models ◽  
Action Theories ◽  
Causal Theories ◽  
Exchange Data

AbstractThere is an increasing interest in using logic programming to specify and implement distributed algorithms, including a variety of network applications. These are applications where data and computation are distributed among several devices and where, in principle, all the devices can exchange data and share the computational results of the group. In this paper we propose a declarative approach to distributed computing whereby distributed algorithms and communication models can be (i) specified as action theories of fluents and actions; (ii) executed as collections of distributed state machines, where devices are abstracted as (input/output) automata that can exchange messages; and (iii) analysed using existing results on connecting causal theories and Answer Set Programming. Results on the application of our approach to different classes of network protocols are also presented.

PROPERTIES OF SELF-REPLICATING CELLULAR AUTOMATA SYSTEMS DISCOVERED USING GENETIC PROGRAMMING

2007 ◽  
Vol 10 (supp01) ◽  
pp. 61-84 ◽  
Author(s):  
ZHIJIAN PAN ◽  
JAMES REGGIA ◽  
DONGHONG GAO
Keyword(s):  
Cellular Automata ◽  
Genetic Programming ◽  
A Priori ◽  
Computation Time ◽  
Initial Configuration ◽  
Number Of Components ◽  
Arbitrary Structure ◽  
Wide Range ◽  
State Changes ◽  
Self Replication

We recently formulated an approach to representing structures in cellular automata (CA) spaces, and the rules that govern cell state changes, that is amenable to manipulation by genetic programming (GP). Using this approach, it is possible to efficiently generate self-replicating configurations for fairly arbitrary initial structures. Here, we investigate the properties of self-replicating systems produced using GP in this fashion as the initial configuration's size, shape, symmetry, allowable states, and other factors are systematically varied. We find that the number of GP generations, computation time, and number of resulting rules required by an arbitrary structure to self-replicate are positively and jointly correlated with the number of components, configuration shape, and allowable states in the initial configuration, but inversely correlated with the presence of repeated components, repeated sub-structures, and/or symmetric sub-structures. We conclude that GP can be used as a "replicator factory" to produce a wide range of self-replicating CA configurations, and that the properties of the resulting replicators can be predicted in part a priori. The rules controlling self-replication that are created by GP generally differ from those created manually in past CA studies.

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