1,893 research outputs found
Degree-constrained Subgraph Reconfiguration is in P
The degree-constrained subgraph problem asks for a subgraph of a given graph
such that the degree of each vertex is within some specified bounds. We study
the following reconfiguration variant of this problem: Given two solutions to a
degree-constrained subgraph instance, can we transform one solution into the
other by adding and removing individual edges, such that each intermediate
subgraph satisfies the degree constraints and contains at least a certain
minimum number of edges? This problem is a generalization of the matching
reconfiguration problem, which is known to be in P. We show that even in the
more general setting the reconfiguration problem is in P.Comment: Full version of the paper published at Mathematical Foundations of
Computer Science (MFCS) 201
41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)
The partial string avoidability problem, also known as partial word avoidability, is stated as follows: given a finite set of strings with possible ``holes'' (undefined symbols), determine whether there exists any two-sided infinite string containing no substrings from this set, assuming that a hole matches every symbol. The problem is known to be NP-hard and in PSPACE, and this paper establishes its PSPACE-completeness. Next, string avoidability over the binary alphabet is interpreted as a version of conjunctive normal form (CNF) satisfiability problem (SAT), with each clause having infinitely many shifted variants. Non-satisfiability of these formulas can be proved using variants of classical propositional proof systems, augmented with derivation rules for shifting constraints (such as clauses, inequalities, polynomials, etc). Two results on their proof complexity are established. First, there is a particular formula that has a short refutation in Resolution with shift, but requires classical proofs of exponential size (Resolution, Cutting Plane, Polynomial Calculus, etc.). At the same time, exponential lower bounds for shifted versions of classical proof systems are established. </p
45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
We consider repetitions in infinite words by making a novel inquiry to the maximum eventual growth rate of the exponents of abelian powers occurring in an infinite word. Given an increasing, unbounded function , we construct an infinite binary word whose abelian exponents have limit superior growth rate . As a consequence, we obtain that every nonnegative real number is the critical abelian exponent of some infinite binary word.</p
On Pebble Automata for Data Languages with Decidable Emptiness Problem
In this paper we study a subclass of pebble automata (PA) for data languages
for which the emptiness problem is decidable. Namely, we introduce the
so-called top view weak PA. Roughly speaking, top view weak PA are weak PA
where the equality test is performed only between the data values seen by the
two most recently placed pebbles. The emptiness problem for this model is
decidable. We also show that it is robust: alternating, nondeterministic and
deterministic top view weak PA have the same recognition power. Moreover, this
model is strong enough to accept all data languages expressible in Linear
Temporal Logic with the future-time operators, augmented with one register
freeze quantifier.Comment: An extended abstract of this work has been published in the
proceedings of the 34th International Symposium on Mathematical Foundations
of Computer Science (MFCS) 2009}, Springer, Lecture Notes in Computer Science
5734, pages 712-72
Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis
Obtaining lower bounds for NP-hard problems has for a long time been an
active area of research. Recent algebraic techniques introduced by Jonsson et
al. (SODA 2013) show that the time complexity of the parameterized SAT()
problem correlates to the lattice of strong partial clones. With this ordering
they isolated a relation such that SAT() can be solved at least as fast
as any other NP-hard SAT() problem. In this paper we extend this method
and show that such languages also exist for the max ones problem
(MaxOnes()) and the Boolean valued constraint satisfaction problem over
finite-valued constraint languages (VCSP()). With the help of these
languages we relate MaxOnes and VCSP to the exponential time hypothesis in
several different ways.Comment: This is an extended version of Relating the Time Complexity of
Optimization Problems in Light of the Exponential-Time Hypothesis, appearing
in Proceedings of the 39th International Symposium on Mathematical
Foundations of Computer Science MFCS 2014 Budapest, August 25-29, 201
Finding and counting vertex-colored subtrees
The problems studied in this article originate from the Graph Motif problem
introduced by Lacroix et al. in the context of biological networks. The problem
is to decide if a vertex-colored graph has a connected subgraph whose colors
equal a given multiset of colors . It is a graph pattern-matching problem
variant, where the structure of the occurrence of the pattern is not of
interest but the only requirement is the connectedness. Using an algebraic
framework recently introduced by Koutis et al., we obtain new FPT algorithms
for Graph Motif and variants, with improved running times. We also obtain
results on the counting versions of this problem, proving that the counting
problem is FPT if M is a set, but becomes W[1]-hard if M is a multiset with two
colors. Finally, we present an experimental evaluation of this approach on real
datasets, showing that its performance compares favorably with existing
software.Comment: Conference version in International Symposium on Mathematical
Foundations of Computer Science (MFCS), Brno : Czech Republic (2010) Journal
Version in Algorithmic
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