42,397 research outputs found
Termination Detection of Local Computations
Contrary to the sequential world, the processes involved in a distributed
system do not necessarily know when a computation is globally finished. This
paper investigates the problem of the detection of the termination of local
computations. We define four types of termination detection: no detection,
detection of the local termination, detection by a distributed observer,
detection of the global termination. We give a complete characterisation
(except in the local termination detection case where a partial one is given)
for each of this termination detection and show that they define a strict
hierarchy. These results emphasise the difference between computability of a
distributed task and termination detection. Furthermore, these
characterisations encompass all standard criteria that are usually formulated :
topological restriction (tree, rings, or triangu- lated networks ...),
topological knowledge (size, diameter ...), and local knowledge to distinguish
nodes (identities, sense of direction). These results are now presented as
corollaries of generalising theorems. As a very special and important case, the
techniques are also applied to the election problem. Though given in the model
of local computations, these results can give qualitative insight for similar
results in other standard models. The necessary conditions involve graphs
covering and quasi-covering; the sufficient conditions (constructive local
computations) are based upon an enumeration algorithm of Mazurkiewicz and a
stable properties detection algorithm of Szymanski, Shi and Prywes
The Computational Power of Beeps
In this paper, we study the quantity of computational resources (state
machine states and/or probabilistic transition precision) needed to solve
specific problems in a single hop network where nodes communicate using only
beeps. We begin by focusing on randomized leader election. We prove a lower
bound on the states required to solve this problem with a given error bound,
probability precision, and (when relevant) network size lower bound. We then
show the bound tight with a matching upper bound. Noting that our optimal upper
bound is slow, we describe two faster algorithms that trade some state
optimality to gain efficiency. We then turn our attention to more general
classes of problems by proving that once you have enough states to solve leader
election with a given error bound, you have (within constant factors) enough
states to simulate correctly, with this same error bound, a logspace TM with a
constant number of unary input tapes: allowing you to solve a large and
expressive set of problems. These results identify a key simplicity threshold
beyond which useful distributed computation is possible in the beeping model.Comment: Extended abstract to appear in the Proceedings of the International
Symposium on Distributed Computing (DISC 2015
Taming Numbers and Durations in the Model Checking Integrated Planning System
The Model Checking Integrated Planning System (MIPS) is a temporal least
commitment heuristic search planner based on a flexible object-oriented
workbench architecture. Its design clearly separates explicit and symbolic
directed exploration algorithms from the set of on-line and off-line computed
estimates and associated data structures. MIPS has shown distinguished
performance in the last two international planning competitions. In the last
event the description language was extended from pure propositional planning to
include numerical state variables, action durations, and plan quality objective
functions. Plans were no longer sequences of actions but time-stamped
schedules. As a participant of the fully automated track of the competition,
MIPS has proven to be a general system; in each track and every benchmark
domain it efficiently computed plans of remarkable quality. This article
introduces and analyzes the most important algorithmic novelties that were
necessary to tackle the new layers of expressiveness in the benchmark problems
and to achieve a high level of performance. The extensions include critical
path analysis of sequentially generated plans to generate corresponding optimal
parallel plans. The linear time algorithm to compute the parallel plan bypasses
known NP hardness results for partial ordering by scheduling plans with respect
to the set of actions and the imposed precedence relations. The efficiency of
this algorithm also allows us to improve the exploration guidance: for each
encountered planning state the corresponding approximate sequential plan is
scheduled. One major strength of MIPS is its static analysis phase that grounds
and simplifies parameterized predicates, functions and operators, that infers
knowledge to minimize the state description length, and that detects domain
object symmetries. The latter aspect is analyzed in detail. MIPS has been
developed to serve as a complete and optimal state space planner, with
admissible estimates, exploration engines and branching cuts. In the
competition version, however, certain performance compromises had to be made,
including floating point arithmetic, weighted heuristic search exploration
according to an inadmissible estimate and parameterized optimization
Efficient detection of periodic orbits in chaotic systems by stabilising transformations
An algorithm for detecting periodic orbits in chaotic systems [Phys. Rev. E,
60 (1999), pp.~6172--6175], which combines the set of stabilising
transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78
(1997), pp.~4733--4736] with a modified semi-implicit Euler iterative scheme
and seeding with periodic orbits of neighbouring periods, has been shown to be
highly efficient when applied to low-dimensional systems. The difficulty in
applying the algorithm to higher-dimensional systems is mainly due to the fact
that the number of the stabilising transformations grows extremely fast with
increasing system dimension. Here we analyse the properties of stabilising
transformations and propose an alternative approach for constructing a smaller
set of transformations. The performance of the new approach is illustrated on
the four-dimentional kicked double rotor map and the six-dimensional system of
three coupled Henon maps
Detecting 2-joins faster
2-joins are edge cutsets that naturally appear in the decomposition of
several classes of graphs closed under taking induced subgraphs, such as
balanced bipartite graphs, even-hole-free graphs, perfect graphs and claw-free
graphs. Their detection is needed in several algorithms, and is the slowest
step for some of them. The classical method to detect a 2-join takes
time where is the number of vertices of the input graph and the number
of its edges. To detect \emph{non-path} 2-joins (special kinds of 2-joins that
are needed in all of the known algorithms that use 2-joins), the fastest known
method takes time . Here, we give an -time algorithm for both
of these problems. A consequence is a speed up of several known algorithms
Local Algorithms for Block Models with Side Information
There has been a recent interest in understanding the power of local
algorithms for optimization and inference problems on sparse graphs. Gamarnik
and Sudan (2014) showed that local algorithms are weaker than global algorithms
for finding large independent sets in sparse random regular graphs. Montanari
(2015) showed that local algorithms are suboptimal for finding a community with
high connectivity in the sparse Erd\H{o}s-R\'enyi random graphs. For the
symmetric planted partition problem (also named community detection for the
block models) on sparse graphs, a simple observation is that local algorithms
cannot have non-trivial performance.
In this work we consider the effect of side information on local algorithms
for community detection under the binary symmetric stochastic block model. In
the block model with side information each of the vertices is labeled
or independently and uniformly at random; each pair of vertices is
connected independently with probability if both of them have the same
label or otherwise. The goal is to estimate the underlying vertex
labeling given 1) the graph structure and 2) side information in the form of a
vertex labeling positively correlated with the true one. Assuming that the
ratio between in and out degree is and the average degree , we characterize three different regimes under which a
local algorithm, namely, belief propagation run on the local neighborhoods,
maximizes the expected fraction of vertices labeled correctly. Thus, in
contrast to the case of symmetric block models without side information, we
show that local algorithms can achieve optimal performance for the block model
with side information.Comment: Due to the limitation "The abstract field cannot be longer than 1,920
characters", the abstract here is shorter than that in the PDF fil
Shift-Symmetric Configurations in Two-Dimensional Cellular Automata: Irreversibility, Insolvability, and Enumeration
The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have been for a long time a central focus of complexity science, and physics.
Here, we introduce group-theoretic concepts to identify and enumerate the symmetric inputs, which result in irreversible system behaviors with undesired effects on many computational tasks. The concept of so-called configuration shift-symmetry is applied on two-dimensional cellular automata as an ideal model of computation. The results show the universal insolvability of ânon-symmetricâ tasks regardless of the transition function. By using a compact enumeration formula and bounding the number of shift-symmetric configurations for a given lattice size, we efficiently calculate how likely a configuration randomly generated from a uniform or density-uniform distribution turns shift-symmetric. Further, we devise an algorithm detecting the presence of shift-symmetry in a configuration.
The enumeration and probability formulas can directly help to lower the minimal expected error for many crucial (non-symmetric) distributed problems, such as leader election, edge detection, pattern recognition, convex hull/minimum bounding rectangle, and encryption. Besides cellular automata, the shift-symmetry analysis can be used to study the non-linear behavior in various synchronous rule-based systems that include inference engines, Boolean networks, neural networks, and systolic arrays
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