Revising Johnson’s table for the 21st century

Figueiredo, Celina M. H. de; Melo, Alexsander Andrade de; Sasaki, Diana; Silva, Ana

doi:10.1016/j.dam.2021.05.021

Cited by 9 publications

(10 citation statements)

References 72 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, to date, there is no published polynomial algorithm to solve the problem. Figueiredo et al revisited Johnson's table recently, and although they still marked the problem as in P , the reference remains "ongoing" [FMS22]. Here as a by-product, we clarify that the Minimum Steiner Tree problem on Circle Graphs is NP-hard.…”

Section: Definition 63 Minimum Steiner Tree Problemmentioning

confidence: 74%

“…The minimum Steiner tree problem on circle graphs has been considered to be in P as indicated by Johnson in 1985 [Joh85]. Recently, Figueiredo et al revisited Johnson's table and still marked the problem as in P [FMS22], while leaving the reference as "ongoing". Here we clarify that the minimum Steiner tree problem on circle graphs is in fact NP-hard, settling this 38-year old open problem.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Men Can't Always be Transformed into Mice: Decision Algorithms and Complexity for Sorting by Symmetric Reversals

Tong¹,

Yu²,

Ziyi³

et al. 2023

Preprint

View full text Add to dashboard Cite

Sorting a permutation by reversals is a famous problem in genome rearrangements, and has been well studied over the past thirty years. But the involvement of repeated segments is inevitable during genome evolution, especially in reversal events. Since 1997, quite some biological evidence were found that in many genomes the reversed regions are usually flanked by a pair of inverted repeats. For example, a reversal will transform +a + x − y − z − a into +a + z + y − x − a, where +a and −a form a pair of inverted repeats.This type of reversals are called symmetric reversals, which, unfortunately, were largely ignored until recently. In this paper, we investigate the problem of sorting by symmetric reversals, which requires a series of symmetric reversals to transform one chromosome A into the another chromosome B. The decision problem of sorting by symmetric reversals is referred to as SSR (when the input chromosomes A and B are given, we use SSR(A,B), similarly for the following optimization version) and the corresponding optimization version (i.e., when the answer for SSR(A,B) is yes, using the minimum number of symmetric reversals to convert A to B), is referred to as SMSR(A,B). The main results of this paper are summarized as follows, where the input is a pair of chromosomes A and B with n repeats.

show abstract

Section: Definition 63 Minimum Steiner Tree Problemmentioning

confidence: 74%

Section: Introductionmentioning

confidence: 99%

Men Can't Always be Transformed into Mice: Decision Algorithms and Complexity for Sorting by Symmetric Reversals

Tong¹,

Yu²,

Ziyi³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…A natural question therefore is whether they are also polynomial‐time solvable on undirected path graphs. This unfortunately is not the case, unless

\mathrm{P}=\mathrm{NP}

, as they are

\mathrm{NP}

‐complete on these graphs [4, 11]. Nevertheless, here we prove that they are FPT when parameterized by

\kappa

on undirected path graphs (Theorem 1 below).…”

Section: Introductionmentioning

confidence: 80%

Parameterized algorithms for Steiner tree and (connected) dominating set on path graphs

de Figueiredo,

Lopes,

de Melo

et al. 2024

Networks

Self Cite

View full text Add to dashboard Cite

Chordal graphs are the intersection graphs of subtrees of a tree, while interval graphs of subpaths of a path. Undirected path graphs, directed path graphs and rooted directed path graphs are intermediate graph classes, defined, respectively, as the intersection graphs of paths of a tree, of directed paths of an oriented tree, and of directed paths of an out branching. All of these path graphs have vertex leafage 2. Dominating Set, Connected Dominating Set, and Steiner tree problems are ‐hard parameterized by the size of the solution on chordal graphs, ‐complete on undirected path graphs, and polynomial‐time solvable on rooted directed path graphs, and hence also on interval graphs. We further investigate the (parameterized) complexity of all these problems when constrained to chordal graphs, taking the vertex leafage and the aforementioned classes into consideration. We prove that Dominating Set, Connected Dominating Set, and Steiner tree are on chordal graphs when parameterized by the size of the solution plus the vertex leafage, and that Weighted Connected Dominating Set is polynomial‐time solvable on strongly chordal graphs. We also introduce a new subclass of undirected path graphs, which we call in–out rooted directed path graphs, as the intersection graphs of directed paths of an in–out branching. We prove that Dominating Set, Connected Dominating Set, and Steiner tree are solvable in polynomial time on this class, generalizing the polynomiality for rooted directed path graphs proved by Booth and Johnson (SIAM J. Comput. 11 (1982), 191‐199.) and by White et al. (Networks 15 (1985), 109‐124.).

show abstract

“…On the other hand, edge‐coloring restricted to planar graphs remains a challenging open problem. Please, refer to [4] for an updated summary table. Surprisingly, after 35 years, the only newly resolved entry for permutation graphs is a Hamiltonian circuit.…”

Section: Introductionmentioning

confidence: 99%

MaxCut on permutation graphs is NP‐complete

Figueiredo

Melo

Oliveira

et al. 2023

Journal of Graph Theory

Self Cite

View full text Add to dashboard Cite

The decision problem MaxC ut is known to be NP‐complete since the seventies, but only recently its restriction to interval graphs has been announced to be hard by Adhikary, Bose, Mukherjee, and Roy. Building on their proof, in this paper we prove that the M axC ut problem is NP‐complete on permutation graphs. This settles a long‐standing open problem that appeared in the 1985 column of the Ongoing Guide to NP‐completeness by David S. Johnson, and is the first NP‐hardness entry for permutation graphs in such column.

show abstract

Revising Johnson’s table for the 21st century

Cited by 9 publications

References 72 publications

Men Can't Always be Transformed into Mice: Decision Algorithms and Complexity for Sorting by Symmetric Reversals

Men Can't Always be Transformed into Mice: Decision Algorithms and Complexity for Sorting by Symmetric Reversals

Parameterized algorithms for Steiner tree and (connected) dominating set on path graphs

MaxCut on permutation graphs is NP‐complete

Contact Info

Product

Resources

About