23 research outputs found
-SAT problem and its applications in dominating set problems
The satisfiability problem is known to be -complete in general
and for many restricted cases. One way to restrict instances of -SAT is to
limit the number of times a variable can be occurred. It was shown that for an
instance of 4-SAT with the property that every variable appears in exactly 4
clauses (2 times negated and 2 times not negated), determining whether there is
an assignment for variables such that every clause contains exactly two true
variables and two false variables is -complete. In this work, we
show that deciding the satisfiability of 3-SAT with the property that every
variable appears in exactly four clauses (two times negated and two times not
negated), and each clause contains at least two distinct variables is -complete. We call this problem -SAT. For an -regular
graph with , it was asked in [Discrete Appl. Math.,
160(15):2142--2146, 2012] to determine whether for a given independent set
there is an independent dominating set that dominates such that ? As an application of -SAT problem we show that
for every , this problem is -complete. Among other
results, we study the relationship between 1-perfect codes and the incidence
coloring of graphs and as another application of our complexity results, we
prove that for a given cubic graph deciding whether is 4-incidence
colorable is -complete
Motioning connected subgraphs into a graph
In this paper we study connected subgraphs and how to motion them inside a
connected graph preserving the connectivity. We determine completely the group
of movements.Comment: 17 pages, 18 figure
Push-Pull Block Puzzles are Hard
This paper proves that push-pull block puzzles in 3D are PSPACE-complete to
solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve,
settling an open question by Zubaran and Ritt. Push-pull block puzzles are a
type of recreational motion planning problem, similar to Sokoban, that involve
moving a `robot' on a square grid with obstacles. The obstacles
cannot be traversed by the robot, but some can be pushed and pulled by the
robot into adjacent squares. Thin walls prevent movement between two adjacent
squares. This work follows in a long line of algorithms and complexity work on
similar problems. The 2D push-pull block puzzle shows up in the video games
Pukoban as well as The Legend of Zelda: A Link to the Past, giving another
proof of hardness for the latter. This variant of block-pushing puzzles is of
particular interest because of its connections to reversibility, since any
action (e.g., push or pull) can be inverted by another valid action (e.g., pull
or push).Comment: Full version of CIAC 2017 paper. 17 page
Shortest Reconfiguration of Sliding Tokens on a Caterpillar
Suppose that we are given two independent sets I_b and I_r of a graph such
that |I_b|=|I_r|, and imagine that a token is placed on each vertex in |I_b|.
Then, the sliding token problem is to determine whether there exists a sequence
of independent sets which transforms I_b into I_r so that each independent set
in the sequence results from the previous one by sliding exactly one token
along an edge in the graph. The sliding token problem is one of the
reconfiguration problems that attract the attention from the viewpoint of
theoretical computer science. The reconfiguration problems tend to be
PSPACE-complete in general, and some polynomial time algorithms are shown in
restricted cases. Recently, the problems that aim at finding a shortest
reconfiguration sequence are investigated. For the 3SAT problem, a trichotomy
for the complexity of finding the shortest sequence has been shown, that is, it
is in P, NP-complete, or PSPACE-complete in certain conditions. In general,
even if it is polynomial time solvable to decide whether two instances are
reconfigured with each other, it can be NP-complete to find a shortest sequence
between them. Namely, finding a shortest sequence between two independent sets
can be more difficult than the decision problem of reconfigurability between
them. In this paper, we show that the problem for finding a shortest sequence
between two independent sets is polynomial time solvable for some graph classes
which are subclasses of the class of interval graphs. More precisely, we can
find a shortest sequence between two independent sets on a graph G in
polynomial time if either G is a proper interval graph, a trivially perfect
graph, or a caterpillar. As far as the authors know, this is the first
polynomial time algorithm for the shortest sliding token problem for a graph
class that requires detours
BHFFA*: Un nuevo algoritmo admisible de búsqueda bidireccional
A pesar de que inicialmente hubo un gran interés en los algoritmos de búsqueda bidireccionales, muy pronto se pensó que garantizar la optimalidad de las soluciones encontradas de este modo era muy complicado, y por ello se desestimó esta lÃnea de investigación. En este artÃculo se muestra, sin embargo, que es posible superar los principales inconvenientes de la búsqueda bidireccional y desarrollar un nuevo algoritmo admisible, con una heurÃstica consistente, y en términos muy sencillos. Además, a diferencia de otras implementaciones bidireccionales, la que se muestra aquà puede resultar en reducciones del tiempo necesario y de la memoria consumida de hasta el 99%, y siempre superior a su implementación unidireccional. Para constatarlo, se han estudiado dos dominios radicalmente diferentes: el grafo del Metro de Madrid y el juego del N-‘Puzle’
Explanation Generation for Multi-Modal Multi-Agent Path Finding with Optimal Resource Utilization using Answer Set Programming
The multi-agent path finding (MAPF) problem is a combinatorial search problem
that aims at finding paths for multiple agents (e.g., robots) in an environment
(e.g., an autonomous warehouse) such that no two agents collide with each
other, and subject to some constraints on the lengths of paths. We consider a
general version of MAPF, called mMAPF, that involves multi-modal transportation
modes (e.g., due to velocity constraints) and consumption of different types of
resources (e.g., batteries). The real-world applications of mMAPF require
flexibility (e.g., solving variations of mMAPF) as well as explainability. Our
earlier studies on mMAPF have focused on the former challenge of flexibility.
In this study, we focus on the latter challenge of explainability, and
introduce a method for generating explanations for queries regarding the
feasibility and optimality of solutions, the nonexistence of solutions, and the
observations about solutions. Our method is based on answer set programming.
This paper is under consideration for acceptance in TPLP.Comment: Paper presented at the 36th International Conference on Logic
Programming (ICLP 2020), University Of Calabria, Rende (CS), Italy, September
2020, 16 pages, 6 figure