370 research outputs found
Randomized Algorithms for the Loop Cutset Problem
We show how to find a minimum weight loop cutset in a Bayesian network with
high probability. Finding such a loop cutset is the first step in the method of
conditioning for inference. Our randomized algorithm for finding a loop cutset
outputs a minimum loop cutset after O(c 6^k kn) steps with probability at least
1 - (1 - 1/(6^k))^c6^k, where c > 1 is a constant specified by the user, k is
the minimal size of a minimum weight loop cutset, and n is the number of
vertices. We also show empirically that a variant of this algorithm often finds
a loop cutset that is closer to the minimum weight loop cutset than the ones
found by the best deterministic algorithms known
Fast Structuring of Radio Networks for Multi-Message Communications
We introduce collision free layerings as a powerful way to structure radio
networks. These layerings can replace hard-to-compute BFS-trees in many
contexts while having an efficient randomized distributed construction. We
demonstrate their versatility by using them to provide near optimal distributed
algorithms for several multi-message communication primitives.
Designing efficient communication primitives for radio networks has a rich
history that began 25 years ago when Bar-Yehuda et al. introduced fast
randomized algorithms for broadcasting and for constructing BFS-trees. Their
BFS-tree construction time was rounds, where is the network
diameter and is the number of nodes. Since then, the complexity of a
broadcast has been resolved to be rounds. On the other hand, BFS-trees have been used as a crucial building
block for many communication primitives and their construction time remained a
bottleneck for these primitives.
We introduce collision free layerings that can be used in place of BFS-trees
and we give a randomized construction of these layerings that runs in nearly
broadcast time, that is, w.h.p. in rounds for any constant . We then use these
layerings to obtain: (1) A randomized algorithm for gathering messages
running w.h.p. in rounds. (2) A randomized -message
broadcast algorithm running w.h.p. in rounds. These
algorithms are optimal up to the small difference in the additive
poly-logarithmic term between and . Moreover, they imply the
first optimal round randomized gossip algorithm
Hitting Diamonds and Growing Cacti
We consider the following NP-hard problem: in a weighted graph, find a
minimum cost set of vertices whose removal leaves a graph in which no two
cycles share an edge. We obtain a constant-factor approximation algorithm,
based on the primal-dual method. Moreover, we show that the integrality gap of
the natural LP relaxation of the problem is \Theta(\log n), where n denotes the
number of vertices in the graph.Comment: v2: several minor changes
Greedy D-Approximation Algorithm for Covering with Arbitrary Constraints and Submodular Cost
This paper describes a simple greedy D-approximation algorithm for any
covering problem whose objective function is submodular and non-decreasing, and
whose feasible region can be expressed as the intersection of arbitrary (closed
upwards) covering constraints, each of which constrains at most D variables of
the problem. (A simple example is Vertex Cover, with D = 2.) The algorithm
generalizes previous approximation algorithms for fundamental covering problems
and online paging and caching problems
How Unsplittable-Flow-Covering helps Scheduling with Job-Dependent Cost Functions
Generalizing many well-known and natural scheduling problems, scheduling with
job-specific cost functions has gained a lot of attention recently. In this
setting, each job incurs a cost depending on its completion time, given by a
private cost function, and one seeks to schedule the jobs to minimize the total
sum of these costs. The framework captures many important scheduling objectives
such as weighted flow time or weighted tardiness. Still, the general case as
well as the mentioned special cases are far from being very well understood
yet, even for only one machine. Aiming for better general understanding of this
problem, in this paper we focus on the case of uniform job release dates on one
machine for which the state of the art is a 4-approximation algorithm. This is
true even for a special case that is equivalent to the covering version of the
well-studied and prominent unsplittable flow on a path problem, which is
interesting in its own right. For that covering problem, we present a
quasi-polynomial time -approximation algorithm that yields an
-approximation for the above scheduling problem. Moreover, for
the latter we devise the best possible resource augmentation result regarding
speed: a polynomial time algorithm which computes a solution with \emph{optimal
}cost at speedup. Finally, we present an elegant QPTAS for the
special case where the cost functions of the jobs fall into at most
many classes. This algorithm allows the jobs even to have up to many
distinct release dates.Comment: 2 pages, 1 figur
Lower Bounds for Structuring Unreliable Radio Networks
In this paper, we study lower bounds for randomized solutions to the maximal
independent set (MIS) and connected dominating set (CDS) problems in the dual
graph model of radio networks---a generalization of the standard graph-based
model that now includes unreliable links controlled by an adversary. We begin
by proving that a natural geographic constraint on the network topology is
required to solve these problems efficiently (i.e., in time polylogarthmic in
the network size). We then prove the importance of the assumption that nodes
are provided advance knowledge of their reliable neighbors (i.e, neighbors
connected by reliable links). Combined, these results answer an open question
by proving that the efficient MIS and CDS algorithms from [Censor-Hillel, PODC
2011] are optimal with respect to their dual graph model assumptions. They also
provide insight into what properties of an unreliable network enable efficient
local computation.Comment: An extended abstract of this work appears in the 2014 proceedings of
the International Symposium on Distributed Computing (DISC
Broadcasting in Noisy Radio Networks
The widely-studied radio network model [Chlamtac and Kutten, 1985] is a
graph-based description that captures the inherent impact of collisions in
wireless communication. In this model, the strong assumption is made that node
receives a message from a neighbor if and only if exactly one of its
neighbors broadcasts.
We relax this assumption by introducing a new noisy radio network model in
which random faults occur at senders or receivers. Specifically, for a constant
noise parameter , either every sender has probability of
transmitting noise or every receiver of a single transmission in its
neighborhood has probability of receiving noise.
We first study single-message broadcast algorithms in noisy radio networks
and show that the Decay algorithm [Bar-Yehuda et al., 1992] remains robust in
the noisy model while the diameter-linear algorithm of Gasieniec et al., 2007
does not. We give a modified version of the algorithm of Gasieniec et al., 2007
that is robust to sender and receiver faults, and extend both this modified
algorithm and the Decay algorithm to robust multi-message broadcast algorithms.
We next investigate the extent to which (network) coding improves throughput
in noisy radio networks. We address the previously perplexing result of Alon et
al. 2014 that worst case coding throughput is no better than worst case routing
throughput up to constants: we show that the worst case throughput performance
of coding is, in fact, superior to that of routing -- by a
gap -- provided receiver faults are introduced. However, we show that any
coding or routing scheme for the noiseless setting can be transformed to be
robust to sender faults with only a constant throughput overhead. These
transformations imply that the results of Alon et al., 2014 carry over to noisy
radio networks with sender faults.Comment: Principles of Distributed Computing 201
Emergence of hyperons in failed supernovae: trigger of the black hole formation
We investigate the emergence of strange baryons in the dynamical collapse of
a non-rotating massive star to a black hole by the neutrino-radiation
hydrodynamical simulations in general relativity. By following the dynamical
formation and collapse of nascent proto-neutron star from the gravitational
collapse of a 40Msun star adopting a new hyperonic EOS table, we show that the
hyperons do not appear at the core bounce but populate quickly at ~0.5-0.7 s
after the bounce to trigger the re-collapse to a black hole. They start to show
up off center owing to high temperatures and later prevail at center when the
central density becomes high enough. The neutrino emission from the accreting
proto-neutron star with the hyperonic EOS stops much earlier than the
corresponding case with a nucleonic EOS while the average energies and
luminosities are quite similar between them. These features of neutrino signal
are a potential probe of the emergence of new degrees of freedom inside the
black hole forming collapse.Comment: 11 pages, 3 figures, accepted for publication in ApJ
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