3,393 research outputs found
Balanced Allocation on Graphs: A Random Walk Approach
In this paper we propose algorithms for allocating sequential balls into
bins that are interconnected as a -regular -vertex graph , where
can be any integer.Let be a given positive integer. In each round
, , ball picks a node of uniformly at random and
performs a non-backtracking random walk of length from the chosen node.Then
it allocates itself on one of the visited nodes with minimum load (ties are
broken uniformly at random). Suppose that has a sufficiently large girth
and . Then we establish an upper bound for the maximum number
of balls at any bin after allocating balls by the algorithm, called {\it
maximum load}, in terms of with high probability. We also show that the
upper bound is at most an factor above the lower bound that is
proved for the algorithm. In particular, we show that if we set , for every constant , and
has girth at least , then the maximum load attained by the
algorithm is bounded by with high probability.Finally, we
slightly modify the algorithm to have similar results for balanced allocation
on -regular graph with and sufficiently large girth
The number of independent sets in a graph with small maximum degree
Let be the number of independent sets in a graph . We show
that if has maximum degree at most then
(where is vertex degree, is the number of isolated
vertices in and is the complete bipartite graph with vertices
in one partition class and in the other), with equality if and only if each
connected component of is either a complete bipartite graph or a single
vertex. This bound (for all ) was conjectured by Kahn.
A corollary of our result is that if is -regular with then with
equality if and only if is a disjoint union of copies of
. This bound (for all ) was conjectured by Alon and Kahn and
recently proved for all by the second author, without the characterization
of the extreme cases.
Our proof involves a reduction to a finite search. For graphs with maximum
degree at most the search could be done by hand, but for the case of
maximum degree or , a computer is needed.Comment: Article will appear in {\em Graphs and Combinatorics
On the Complexity of Local Distributed Graph Problems
This paper is centered on the complexity of graph problems in the
well-studied LOCAL model of distributed computing, introduced by Linial [FOCS
'87]. It is widely known that for many of the classic distributed graph
problems (including maximal independent set (MIS) and -vertex
coloring), the randomized complexity is at most polylogarithmic in the size
of the network, while the best deterministic complexity is typically
. Understanding and narrowing down this exponential gap
is considered to be one of the central long-standing open questions in the area
of distributed graph algorithms. We investigate the problem by introducing a
complexity-theoretic framework that allows us to shed some light on the role of
randomness in the LOCAL model. We define the SLOCAL model as a sequential
version of the LOCAL model. Our framework allows us to prove completeness
results with respect to the class of problems which can be solved efficiently
in the SLOCAL model, implying that if any of the complete problems can be
solved deterministically in rounds in the LOCAL model, we can
deterministically solve all efficient SLOCAL-problems (including MIS and
-coloring) in rounds in the LOCAL model. We show
that a rather rudimentary looking graph coloring problem is complete in the
above sense: Color the nodes of a graph with colors red and blue such that each
node of sufficiently large polylogarithmic degree has at least one neighbor of
each color. The problem admits a trivial zero-round randomized solution. The
result can be viewed as showing that the only obstacle to getting efficient
determinstic algorithms in the LOCAL model is an efficient algorithm to
approximately round fractional values into integer values
Irrelevance in Problem Solving
The notion of irrelevance underlies many different works in AI, such as detecting redundant facts, creating abstraction hierarchies and reformulation and modeling physical devices. However, in order to design problem solvers that exploit the notion of irrelevance, either by automatically detecting irrelevance or by being given knowledge about irrelevance, a formal treatment of the notion is required. In this paper we present a general framework for analyzing irrelevance. We discuss several properties of irrelevance and show how they vary in a space of definitions outlined by the framework. We show how irrelevance claims can be used to justify the creation of abstractions thereby suggesting a new view on the work on abstraction
Fouling mechanisms in constant flux crossflow ultrafiltration
Four fouling models due to Hermia (complete pore blocking, intermediate pore blocking, cake filtration and standard pore blocking), have long been used to describe membrane filtration and fouling in constant transmembrane pressure (ΔP) operation of membranes. A few studies apply these models to constant flux dead-end filtration systems. However, these models have not been reported for constant flux crossflow filtration, despite the frequent use of this mode of membrane operation in practical applications. We report derivation of these models for constant flux crossflow filtration. Of the four models, complete pore blocking and standard pore blocking were deemed inapplicable due to contradicting assumptions and relevance, respectively. Constant flux crossflow fouling experiments of dilute latex bead suspensions and soybean oil emulsions were conducted on commercial poly (ether sulfone) flat sheet ultrafiltration membranes to explore the models’ abilities to describe such data. A model combining intermediate pore blocking and cake filtration appeared to give the best agreement with the experimental data. Below the threshold flux, both the intermediate pore blocking model and the combined model fit the data well. As permeate flux approached and passed the threshold flux, the combined model was required for accurate fits. Based on this observation, a physical interpretation of the threshold flux is proposed: the threshold flux is the flux below which cake buildup is negligible and above which cake filtration becomes the dominant fouling mechanism
T Cell-Mediated Modulation of Mast Cell Function: Heterotypic Adhesion-Induced Stimulatory or Inhibitory Effects
Close physical proximity between mast cells and T cells has been demonstrated in several T cell mediated inflammatory processes such as rheumatoid arthritis and sarcoidosis. However, the way by which mast cells are activated in these T cell-mediated immune responses has not been fully elucidated. We have identified and characterized a novel mast cell activation pathway initiated by physical contact with activated T cells, and showed that this pathway is associated with degranulation and cytokine release. The signaling events associated with this pathway of mast cell activation have also been elucidated confirming the activation of the Ras mitogen-activated protein kinase systems. More recently, we hypothesized and demonstrated that mast cells may also be activated by microparticles released from activated T cells that are considered as miniature version of a cell. By extension, microparticles might affect the activity of mast cells, which are usually not in direct contact with T cells at the inflammatory site. Recent works have also focused on the effects of regulatory T cells (Treg) on mast cells. These reports highlighted the importance of the cytokines IL-2 and IL-9, produced by mast cells and T cells, respectively, in obtaining optimal immune suppression. Finally, physical contact, associated by OX40–OX40L engagement has been found to underlie the down-regulatory effects exerted by Treg on mast cell function
High degree graphs contain large-star factors
We show that any finite simple graph with minimum degree contains a
spanning star forest in which every connected component is of size at least
. This settles a problem of J. Kratochvil
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