2,901 research outputs found
Self-stabilizing algorithms for Connected Vertex Cover and Clique decomposition problems
In many wireless networks, there is no fixed physical backbone nor
centralized network management. The nodes of such a network have to
self-organize in order to maintain a virtual backbone used to route messages.
Moreover, any node of the network can be a priori at the origin of a malicious
attack. Thus, in one hand the backbone must be fault-tolerant and in other hand
it can be useful to monitor all network communications to identify an attack as
soon as possible. We are interested in the minimum \emph{Connected Vertex
Cover} problem, a generalization of the classical minimum Vertex Cover problem,
which allows to obtain a connected backbone. Recently, Delbot et
al.~\cite{DelbotLP13} proposed a new centralized algorithm with a constant
approximation ratio of for this problem. In this paper, we propose a
distributed and self-stabilizing version of their algorithm with the same
approximation guarantee. To the best knowledge of the authors, it is the first
distributed and fault-tolerant algorithm for this problem. The approach
followed to solve the considered problem is based on the construction of a
connected minimal clique partition. Therefore, we also design the first
distributed self-stabilizing algorithm for this problem, which is of
independent interest
Survey of Distributed Decision
We survey the recent distributed computing literature on checking whether a
given distributed system configuration satisfies a given boolean predicate,
i.e., whether the configuration is legal or illegal w.r.t. that predicate. We
consider classical distributed computing environments, including mostly
synchronous fault-free network computing (LOCAL and CONGEST models), but also
asynchronous crash-prone shared-memory computing (WAIT-FREE model), and mobile
computing (FSYNC model)
Local algorithms : Self-stabilization on speed
Non peer reviewe
Design of Self-Stabilizing Approximation Algorithms via a Primal-Dual Approach
Self-stabilization is an important concept in the realm of fault-tolerant distributed computing. In this paper, we propose a new approach that relies on the properties of linear programming duality to obtain self-stabilizing approximation algorithms for distributed graph optimization problems. The power of this new approach is demonstrated by the following results:
- A self-stabilizing 2(1+?)-approximation algorithm for minimum weight vertex cover that converges in O(log? /(?log log ?)) synchronous rounds.
- A self-stabilizing ?-approximation algorithm for maximum weight independent set that converges in O(?+log^* n) synchronous rounds.
- A self-stabilizing ((2?+1)(1+?))-approximation algorithm for minimum weight dominating set in ?-arboricity graphs that converges in O((log?)/?) synchronous rounds. In all of the above, ? denotes the maximum degree. Our technique improves upon previous results in terms of time complexity while incurring only an additive O(log n) overhead to the message size. In addition, to the best of our knowledge, we provide the first self-stabilizing algorithms for the weighted versions of minimum vertex cover and maximum independent set
The difficulty of folding self-folding origami
Why is it difficult to refold a previously folded sheet of paper? We show
that even crease patterns with only one designed folding motion inevitably
contain an exponential number of `distractor' folding branches accessible from
a bifurcation at the flat state. Consequently, refolding a sheet requires
finding the ground state in a glassy energy landscape with an exponential
number of other attractors of higher energy, much like in models of protein
folding (Levinthal's paradox) and other NP-hard satisfiability (SAT) problems.
As in these problems, we find that refolding a sheet requires actuation at
multiple carefully chosen creases. We show that seeding successful folding in
this way can be understood in terms of sub-patterns that fold when cut out
(`folding islands'). Besides providing guidelines for the placement of active
hinges in origami applications, our results point to fundamental limits on the
programmability of energy landscapes in sheets.Comment: 8 pages, 5 figure
Lattice Linear Problems vs Algorithms
Modelling problems using predicates that induce a partial order among global
states was introduced as a way to permit asynchronous execution in
multiprocessor systems. A key property of such problems is that the predicate
induces one lattice in the state space which guarantees that the execution is
correct even if nodes execute with old information about their neighbours.
Thus, a compiler that is aware of this property can ignore data dependencies
and allow the application to continue its execution with the available data
rather than waiting for the most recent one. Unfortunately, many interesting
problems do not exhibit lattice linearity. This issue was alleviated with the
introduction of eventually lattice linear algorithms. Such algorithms induce a
partial order in a subset of the state space even though the problem cannot be
defined by a predicate under which the states form a partial order.
This paper focuses on analyzing and differentiating between lattice linear
problems and algorithms. It also introduces a new class of algorithms called
(fully) lattice linear algorithms. A characteristic of these algorithms is that
the entire reachable state space is partitioned into one or more lattices and
the initial state locks into one of these lattices. Thus, under a few
additional constraints, the initial state can uniquely determine the final
state. For demonstration, we present lattice linear self-stabilizing algorithms
for minimal dominating set and graph colouring problems, and a parallel
processing 2-approximation algorithm for vertex cover.
The algorithm for minimal dominating set converges in n moves, and that for
graph colouring converges in n+2m moves. The algorithm for vertex cover is the
first lattice linear approximation algorithm for an NP-Hard problem; it
converges in n moves.
Some part is cut due to 1920 character limit. Please see the pdf for full
abstract.Comment: arXiv admin note: text overlap with arXiv:2209.1470
Approximating max-min linear programs with local algorithms
A local algorithm is a distributed algorithm where each node must operate
solely based on the information that was available at system startup within a
constant-size neighbourhood of the node. We study the applicability of local
algorithms to max-min LPs where the objective is to maximise subject to for each and
for each . Here , , and the support sets , ,
and have bounded size. In the distributed setting,
each agent is responsible for choosing the value of , and the
communication network is a hypergraph where the sets and
constitute the hyperedges. We present inapproximability results for a
wide range of structural assumptions; for example, even if and
are bounded by some constants larger than 2, there is no local approximation
scheme. To contrast the negative results, we present a local approximation
algorithm which achieves good approximation ratios if we can bound the relative
growth of the vertex neighbourhoods in .Comment: 16 pages, 2 figure
Domination parameters with number 2: interrelations and algorithmic consequences
In this paper, we study the most basic domination invariants in graphs, in
which number 2 is intrinsic part of their definitions. We classify them upon
three criteria, two of which give the following previously studied invariants:
the weak -domination number, , the -domination number,
, the -domination number, , the double
domination number, , the total -domination number,
, and the total double domination number, , where is a graph in which a corresponding invariant is well
defined. The third criterion yields rainbow versions of the mentioned six
parameters, one of which has already been well studied, and three other give
new interesting parameters. Together with a special, extensively studied Roman
domination, , and two classical parameters, the domination number,
, and the total domination number, , we consider 13
domination invariants in graphs . In the main result of the paper we present
sharp upper and lower bounds of each of the invariants in terms of every other
invariant, large majority of which are new results proven in this paper. As a
consequence of the main theorem we obtain some complexity results for the
studied invariants, in particular regarding the existence of approximation
algorithms and inapproximability bounds.Comment: 45 pages, 4 tables, 7 figure
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