58,853 research outputs found
Markov Chain Monitoring
In networking applications, one often wishes to obtain estimates about the
number of objects at different parts of the network (e.g., the number of cars
at an intersection of a road network or the number of packets expected to reach
a node in a computer network) by monitoring the traffic in a small number of
network nodes or edges. We formalize this task by defining the 'Markov Chain
Monitoring' problem.
Given an initial distribution of items over the nodes of a Markov chain, we
wish to estimate the distribution of items at subsequent times. We do this by
asking a limited number of queries that retrieve, for example, how many items
transitioned to a specific node or over a specific edge at a particular time.
We consider different types of queries, each defining a different variant of
the Markov chain monitoring. For each variant, we design efficient algorithms
for choosing the queries that make our estimates as accurate as possible. In
our experiments with synthetic and real datasets we demonstrate the efficiency
and the efficacy of our algorithms in a variety of settings.Comment: 13 pages, 10 figures, 1 tabl
The complexity of dominating set reconfiguration
Suppose that we are given two dominating sets and of a graph
whose cardinalities are at most a given threshold . Then, we are asked
whether there exists a sequence of dominating sets of between and
such that each dominating set in the sequence is of cardinality at most
and can be obtained from the previous one by either adding or deleting
exactly one vertex. This problem is known to be PSPACE-complete in general. In
this paper, we study the complexity of this decision problem from the viewpoint
of graph classes. We first prove that the problem remains PSPACE-complete even
for planar graphs, bounded bandwidth graphs, split graphs, and bipartite
graphs. We then give a general scheme to construct linear-time algorithms and
show that the problem can be solved in linear time for cographs, trees, and
interval graphs. Furthermore, for these tractable cases, we can obtain a
desired sequence such that the number of additions and deletions is bounded by
, where is the number of vertices in the input graph
Algorithmic aspects of disjunctive domination in graphs
For a graph , a set is called a \emph{disjunctive
dominating set} of if for every vertex , is either
adjacent to a vertex of or has at least two vertices in at distance
from it. The cardinality of a minimum disjunctive dominating set of is
called the \emph{disjunctive domination number} of graph , and is denoted by
. The \textsc{Minimum Disjunctive Domination Problem} (MDDP)
is to find a disjunctive dominating set of cardinality .
Given a positive integer and a graph , the \textsc{Disjunctive
Domination Decision Problem} (DDDP) is to decide whether has a disjunctive
dominating set of cardinality at most . In this article, we first propose a
linear time algorithm for MDDP in proper interval graphs. Next we tighten the
NP-completeness of DDDP by showing that it remains NP-complete even in chordal
graphs. We also propose a -approximation
algorithm for MDDP in general graphs and prove that MDDP can not be
approximated within for any unless NP
DTIME. Finally, we show that MDDP is
APX-complete for bipartite graphs with maximum degree
Typical and large-deviation properties of minimum-energy paths on disordered hierarchical lattices
We perform numerical simulations to study the optimal path problem on
disordered hierarchical graphs with effective dimension d=2.32. Therein, edge
energies are drawn from a disorder distribution that allows for positive and
negative energies. This induces a behavior which is fundamentally different
from the case where all energies are positive, only. Upon changing the
subtleties of the distribution, the scaling of the minimum energy path length
exhibits a transition from self-affine to self-similar. We analyze the precise
scaling of the path length and the associated ground-state energy fluctuations
in the vincinity of the disorder critical point, using a decimation procedure
for huge graphs. Further, using an importance sampling procedure in the
disorder we compute the negative-energy tails of the ground-state energy
distribution up to 12 standard deviations away from its mean. We find that the
asymptotic behavior of the negative-energy tail is in agreement with a
Tracy-Widom distribution. Further, the characteristic scaling of the tail can
be related to the ground-state energy flucutations, similar as for the directed
polymer in a random medium.Comment: 10 pages, 10 figures, 3 table
Fast Search for Dynamic Multi-Relational Graphs
Acting on time-critical events by processing ever growing social media or
news streams is a major technical challenge. Many of these data sources can be
modeled as multi-relational graphs. Continuous queries or techniques to search
for rare events that typically arise in monitoring applications have been
studied extensively for relational databases. This work is dedicated to answer
the question that emerges naturally: how can we efficiently execute a
continuous query on a dynamic graph? This paper presents an exact subgraph
search algorithm that exploits the temporal characteristics of representative
queries for online news or social media monitoring. The algorithm is based on a
novel data structure called the Subgraph Join Tree (SJ-Tree) that leverages the
structural and semantic characteristics of the underlying multi-relational
graph. The paper concludes with extensive experimentation on several real-world
datasets that demonstrates the validity of this approach.Comment: SIGMOD Workshop on Dynamic Networks Management and Mining (DyNetMM),
201
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