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Token Sliding on Split Graphs [article]

Rémy Belmonte, Eun Jung Kim, Michael Lampis, Valia Mitsou, Yota Otachi, Florian Sikora
2019 arXiv   pre-print
We consider the complexity of the Independent Set Reconfiguration problem under the Token Sliding rule.  ...  Our main result is to show that this problem is PSPACE-complete on split graphs (and hence also on chordal graphs), thus resolving an open problem in this area.  ...  Using XX:6 Token Sliding on Split Graphs these we can force the OR vertices to become an independent set. Lemma 3.  ... 
arXiv:1807.05322v2 fatcat:45ooim6lvbbijddgfbt4ih5czq

Token Sliding on Split Graphs

Rémy Belmonte, Eun Jung Kim, Michael Lampis, Valia Mitsou, Yota Otachi, Florian Sikora, Michael Wagner
2019 Symposium on Theoretical Aspects of Computer Science  
We consider the complexity of the Independent Set Reconfiguration problem under the Token Sliding rule.  ...  Our main result is to show that this problem is PSPACE-complete on split graphs (and hence also on chordal graphs), thus resolving an open problem in this area.  ...  S TA C S 2 0 1 9 13:6 Token Sliding on Split Graphs Proof.  ... 
doi:10.4230/lipics.stacs.2019.13 dblp:conf/stacs/Belmonte0LMOS19 fatcat:4d7q5iqwknfbflkr4u3kranw5u

Reconfiguration of Satisfying Assignments and Subset Sums: Easy to Find, Hard to Connect [article]

Jean Cardinal and Erik D. Demaine and David Eppstein and Robert A. Hearn and Andrew Winslow
2018 arXiv   pre-print
We consider the computational complexity of reconfiguration problems, in which one is given two combinatorial configurations satisfying some constraints, and is asked to transform one into the other using  ...  ∙ Given two subsets of a set S of integers with the same sum, can one subset be transformed into the other by adding or removing at most three elements of S at a time, such that the intermediate subsets  ...  This work was initiated at the 32nd Bellairs Winter Workshop on Computational Geometry, January 27-February 3, 2017.  ... 
arXiv:1805.04055v1 fatcat:7pssuf7g6zbpxcvownrbobgnim

Token Sliding on Chordal Graphs [article]

Marthe Bonamy, Nicolas Bousquet
2016 arXiv   pre-print
In 2014, Demaine et al. asked whether the Token Sliding reconfiguration problem is polynomial time solvable on interval graphs and more generally in chordal graphs.  ...  time; (ii) deciding this problem becomes co-NP-hard and even co-W[2]-hard (parameterized by the size of the independent set) on split graphs, a sub-class of chordal graphs.  ...  TOKEN SLIDING IN SPLIT GRAPHS On the positive side, we show that the connectivity of T S k (G) can be decided in polynomial in interval graphs. Theorem 2.  ... 
arXiv:1605.00442v1 fatcat:hndtwohscbcivjruddkeqjw5mm

Dominating sets reconfiguration under token sliding [article]

Marthe Bonamy
2021 arXiv   pre-print
We first prove that this problem is PSPACE-complete, even when restricted to split, bipartite or bounded treewidth graphs.  ...  On the other hand, we prove that it can be solved in polynomial time on dually chordal graphs (a superclass of both trees and interval graphs) or cographs.  ...  Token Jumping (TJ): one can move a token to any vertex of the graph; 3. Token Sliding (TS): one can slide a token along an edge, i.e., one moves a token to a neighbor of its current location.  ... 
arXiv:1912.03127v2 fatcat:kbl7gan6e5d63nsnvaidbcdgva

Shortest Reconfiguration of Sliding Tokens on a Caterpillar [article]

Takeshi Yamada, Ryuhei Uehara
2015 arXiv   pre-print
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.  ...  . , p k ) splits G into G 1 and G 2 , the neighbors of G 1 and G 2 in P are p 2 and p k−1 , and there are no token on them.  ... 
arXiv:1511.00243v1 fatcat:fpk5fggwsjh5tglp6knjg2dnbe

Galactic Token Sliding [article]

Valentin Bartier and Nicolas Bousquet and Amer E. Mouawad
2022 arXiv   pre-print
In the token sliding variant, a token is only allowed to slide from a vertex to one of its neighbors.  ...  Viewing each independent set as a collection of k tokens placed on the vertices of a graph G, the two most studied reconfiguration steps are token jumping and token sliding.  ...  Token Sliding parameterized by k is W [1] -hard on split graphs.  ... 
arXiv:2204.05549v1 fatcat:ho7jwxgeivb3phoixmjyhm26rm

Token sliding on graphs of girth five [article]

Valentin Bartier and Nicolas Bousquet and Jihad Hanna and Amer E. Mouawad and Sebastian Siebertz
2022 arXiv   pre-print
Sliding parameterized by the number of tokens based on the girth of the input graph.  ...  In the Token Sliding problem we are given a graph G and two independent sets I_s and I_t in G of size k ≥ 1.  ...  On the positive side, it is "easy" to show that Token Jumping can be decided in polynomial-time on trees (and even on split/chordal graphs) since we can simply jump tokens to leaves (resp. vertices that  ... 
arXiv:2205.01009v1 fatcat:3ji6cdxejbf47pbsswj5mmgnme

On Reconfiguration Graph of Independent Sets under Token Sliding [article]

David Avis, Duc A. Hoang
2022 arXiv   pre-print
Two nodes are adjacent if one can be obtained from the other by sliding a token on some vertex to one of its unoccupied neighbors.  ...  An independent set of a graph G is a vertex subset I such that there is no edge joining any two vertices in I. Imagine that a token is placed on each vertex of an independent set of G.  ...  One of the classic reconfiguration rules is the so-called Token Sliding (TS). Any vertex subset of a graph G can be seen as a set of tokens placed on some vertices of G.  ... 
arXiv:2203.16861v1 fatcat:4znzlbij4bbironjear3cccmne

A survey on the parameterized complexity of the independent set and (connected) dominating set reconfiguration problems [article]

Nicolas Bousquet and Amer E. Mouawad and Naomi Nishimura and Sebastian Siebertz
2022 arXiv   pre-print
A graph vertex-subset problem defines which subsets of the vertices of an input graph are feasible solutions. We view a feasible solution as a set of tokens placed on the vertices of the graph.  ...  A reconfiguration variant of a vertex-subset problem asks, given two feasible solutions of size k, whether it is possible to transform one into the other by a sequence of token slides (along edges of the  ...  Independent set reconfiguration under token sliding Just like the token jumping variant, ISR-TS is W[1]-hard on general graphs.  ... 
arXiv:2204.10526v1 fatcat:ua3pkqxtabatbbl6jydhy3i3b4

PSPACE-Completeness of Sliding-Block Puzzles and Other Problems through the Nondeterministic Constraint Logic Model of Computation [article]

Robert A. Hearn, Erik D. Demaine
2004 arXiv   pre-print
We present a nondeterministic model of computation based on reversing edge directions in weighted directed graphs with minimum in-flow constraints on vertices.  ...  Our main result along these lines is that classic unrestricted sliding-block puzzles are PSPACE-hard, even if the pieces are restricted to be all dominoes (1x2 blocks) and the goal is simply to move a  ...  Likewise, the upper token in the Or gadget can slide in when either lower token is slid out -the internal token can then slide to one side or the other to make room.  ... 
arXiv:cs/0205005v5 fatcat:ozdyozcsgnh3fl2imiknvudany

PSPACE-completeness of sliding-block puzzles and other problems through the nondeterministic constraint logic model of computation

Robert A. Hearn, Erik D. Demaine
2005 Theoretical Computer Science  
We present a nondeterministic model of computation based on reversing edge directions in weighted directed graphs with minimum in-flow constraints on vertices.  ...  Our main result along these lines is that classic unrestricted sliding-block puzzles are PSPACE-hard, even if the pieces are restricted to be all dominoes (1 × 2 blocks) and the goal is simply to move  ...  Likewise, the upper token in the OR gadget can slide in when either lower token is slid out-the internal token can then slide to one side or the other to make room.  ... 
doi:10.1016/j.tcs.2005.05.008 fatcat:eyqmplmhanfhxmoiryj4da44ym

Introduction to Reconfiguration

Naomi Nishimura
2018 Algorithms  
Work in the area encompasses both structural questions (Is the reconfiguration graph connected?) and algorithmic ones (How can one find the shortest sequence of steps between two solutions?)  ...  The solution space can be represented as a reconfiguration graph, where two vertices representing solutions are adjacent if one can be formed from the other in a single step.  ...  Both token sliding and token jumping can be viewed as the replacement of a vertex in one solution with a vertex outside the solution.  ... 
doi:10.3390/a11040052 fatcat:nmokeftdqrgtpdyh2ohl3tchce

Independent set reconfiguration on directed graphs [article]

Takehiro Ito, Yuni Iwamasa, Yasuaki Kobayashi, Yu Nakahata, Yota Otachi, Masahiro Takahashi, Kunihiro Wasa
2022 arXiv   pre-print
Directed Token Sliding asks, given a directed graph and two sets of pairwise nonadjacent vertices, whether one can reach from one set to the other by repeatedly applying a local operation that exchanges  ...  It can be seen as a reconfiguration process where a token is placed on each vertex in the current set, and the local operation slides a token along an arc respecting its direction.  ...  The problem is also PSPACE-complete on bipartite graphs [28] and split graphs [3] .  ... 
arXiv:2203.13435v1 fatcat:pdpj67pcarbnvhufztnykcagn4

Preface of STACS 2019 Special Issue

Rolf Niedermeier, Christophe Paul
2021 Theory of Computing Systems  
This special issue contains five articles which are based on extended abstracts presented at the 35th Symposium on Theoretical Aspects of Computer Science (STACS).  ...  The topics of the chosen papers cover various areas of Theoretical Computer Science, that is, algorithmic graph theory, automata theory, linear dynamical systems, parameterized complexity analysis, and  ...  is PSPACE-complete on split graphs (and hence on chordal graphs), a question that has remained unanswered for a few years.  ... 
doi:10.1007/s00224-020-10026-5 fatcat:s3c34bdj45gqplrgpkyhfis244
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