154,136 research outputs found
Recognizing when a preference system is close to admitting a master list
A preference system is an undirected graph where vertices have
preferences over their neighbors, and admits a master list if all
preferences can be derived from a single ordering over all vertices. We study
the problem of deciding whether a given preference system is
close to admitting a master list based on three different distance measures. We
determine the computational complexity of the following questions: can
be modified by (i) swaps in the preferences, (ii) edge
deletions, or (iii) vertex deletions so that the resulting instance admits
a master list? We investigate these problems in detail from the viewpoint of
parameterized complexity and of approximation. We also present two applications
related to stable and popular matchings.Comment: 30 pages, 1 figure. Reason for update: additional discussion on the
Kemeny Score problem, and correction of some typo
Fast algorithms for consistency-based diagnosis of firewall rule sets
Firewalls provide the first line of defence of nearly
all networked institutions today. However, Firewall
ACL management suffer some problems that need to be
addressed in order to be effective. The most studied
one is rule set consistency. There is an inconsistency if
different actions can be taken on the same traffic,
depending on the ordering of the rules. In this paper a
new algorithm to diagnose inconsistencies in firewall
rule sets is presented. Although many algorithms have
been proposed to address this problem, the presented
one is a big improvement over them, due to its low
algorithmic and memory complexity, even in worst
case. In addition, there is no need to pre-process in
any way the rule set previous to the application of the
algorithms. We also present experimental results with
real rule sets that validate our proposal.Ministerio de Educación y Ciencia DPI2006-15476-C02-0
Compilability of Abduction
Abduction is one of the most important forms of reasoning; it has been
successfully applied to several practical problems such as diagnosis. In this
paper we investigate whether the computational complexity of abduction can be
reduced by an appropriate use of preprocessing. This is motivated by the fact
that part of the data of the problem (namely, the set of all possible
assumptions and the theory relating assumptions and manifestations) are often
known before the rest of the problem. In this paper, we show some complexity
results about abduction when compilation is allowed
Dynamic Complexity of Planar 3-connected Graph Isomorphism
Dynamic Complexity (as introduced by Patnaik and Immerman) tries to express
how hard it is to update the solution to a problem when the input is changed
slightly. It considers the changes required to some stored data structure
(possibly a massive database) as small quantities of data (or a tuple) are
inserted or deleted from the database (or a structure over some vocabulary).
The main difference from previous notions of dynamic complexity is that instead
of treating the update quantitatively by finding the the time/space trade-offs,
it tries to consider the update qualitatively, by finding the complexity class
in which the update can be expressed (or made). In this setting, DynFO, or
Dynamic First-Order, is one of the smallest and the most natural complexity
class (since SQL queries can be expressed in First-Order Logic), and contains
those problems whose solutions (or the stored data structure from which the
solution can be found) can be updated in First-Order Logic when the data
structure undergoes small changes.
Etessami considered the problem of isomorphism in the dynamic setting, and
showed that Tree Isomorphism can be decided in DynFO. In this work, we show
that isomorphism of Planar 3-connected graphs can be decided in DynFO+ (which
is DynFO with some polynomial precomputation). We maintain a canonical
description of 3-connected Planar graphs by maintaining a database which is
accessed and modified by First-Order queries when edges are added to or deleted
from the graph. We specifically exploit the ideas of Breadth-First Search and
Canonical Breadth-First Search to prove the results. We also introduce a novel
method for canonizing a 3-connected planar graph in First-Order Logic from
Canonical Breadth-First Search Trees
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