4,312 research outputs found
Finding long cycles in graphs
We analyze the problem of discovering long cycles inside a graph. We propose
and test two algorithms for this task. The first one is based on recent
advances in statistical mechanics and relies on a message passing procedure.
The second follows a more standard Monte Carlo Markov Chain strategy. Special
attention is devoted to Hamiltonian cycles of (non-regular) random graphs of
minimal connectivity equal to three
Multi-Layer Cyber-Physical Security and Resilience for Smart Grid
The smart grid is a large-scale complex system that integrates communication
technologies with the physical layer operation of the energy systems. Security
and resilience mechanisms by design are important to provide guarantee
operations for the system. This chapter provides a layered perspective of the
smart grid security and discusses game and decision theory as a tool to model
the interactions among system components and the interaction between attackers
and the system. We discuss game-theoretic applications and challenges in the
design of cross-layer robust and resilient controller, secure network routing
protocol at the data communication and networking layers, and the challenges of
the information security at the management layer of the grid. The chapter will
discuss the future directions of using game-theoretic tools in addressing
multi-layer security issues in the smart grid.Comment: 16 page
Hybrid Behaviour of Markov Population Models
We investigate the behaviour of population models written in Stochastic
Concurrent Constraint Programming (sCCP), a stochastic extension of Concurrent
Constraint Programming. In particular, we focus on models from which we can
define a semantics of sCCP both in terms of Continuous Time Markov Chains
(CTMC) and in terms of Stochastic Hybrid Systems, in which some populations are
approximated continuously, while others are kept discrete. We will prove the
correctness of the hybrid semantics from the point of view of the limiting
behaviour of a sequence of models for increasing population size. More
specifically, we prove that, under suitable regularity conditions, the sequence
of CTMC constructed from sCCP programs for increasing population size converges
to the hybrid system constructed by means of the hybrid semantics. We
investigate in particular what happens for sCCP models in which some
transitions are guarded by boolean predicates or in the presence of
instantaneous transitions
Improved Approximation Algorithms for Stochastic Matching
In this paper we consider the Stochastic Matching problem, which is motivated
by applications in kidney exchange and online dating. We are given an
undirected graph in which every edge is assigned a probability of existence and
a positive profit, and each node is assigned a positive integer called timeout.
We know whether an edge exists or not only after probing it. On this random
graph we are executing a process, which one-by-one probes the edges and
gradually constructs a matching. The process is constrained in two ways: once
an edge is taken it cannot be removed from the matching, and the timeout of
node upper-bounds the number of edges incident to that can be probed.
The goal is to maximize the expected profit of the constructed matching.
For this problem Bansal et al. (Algorithmica 2012) provided a
-approximation algorithm for bipartite graphs, and a -approximation for
general graphs. In this work we improve the approximation factors to
and , respectively.
We also consider an online version of the bipartite case, where one side of
the partition arrives node by node, and each time a node arrives we have to
decide which edges incident to we want to probe, and in which order. Here
we present a -approximation, improving on the -approximation of
Bansal et al.
The main technical ingredient in our result is a novel way of probing edges
according to a random but non-uniform permutation. Patching this method with an
algorithm that works best for large probability edges (plus some additional
ideas) leads to our improved approximation factors
Effects of Diversity and Procrastination in Priority Queuing Theory: the Different Power Law Regimes
Empirical analysis show that, after the update of a browser, the publication
of the vulnerability of a software, or the discovery of a cyber worm, the
fraction of computers still using the older version, or being not yet patched,
or exhibiting worm activity decays as power laws with over time scales of years. We present a simple model for this
persistence phenomenon framed within the standard priority queuing theory, of a
target task which has the lowest priority compared with all other tasks that
flow on the computer of an individual. We identify a "time deficit" control
parameter and a bifurcation to a regime where there is a non-zero
probability for the target task to never be completed. The distribution of
waiting time till the completion of the target task has the power
law tail , resulting from a first-passage solution of an
equivalent Wiener process. Taking into account a diversity of time deficit
parameters in a population of individuals, the power law tail is changed into
with , including the well-known case .
We also study the effect of "procrastination", defined as the situation in
which the target task may be postponed or delayed even after the individual has
solved all other pending tasks. This new regime provides an explanation for
even slower apparent decay and longer persistence.Comment: 32 pages, 10 figure
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