Home Knowledge Base NP-Complete

NP-Complete

No mentions found

This entity hasn't been tracked yet, or Iris is still building its knowledge base.

Related Articles from SNS

Structures preserved by primitive actions of $S_\omega$

arXiv:2501.03789v4 Announce Type: replace-cross Abstract: We present a dichotomy for structures $A$ that are preserved by primitive actions of $S_{\omega} = \text{Sym}({\mathbb N})$: such a structure primitively positively constructs all finite structures and the constraint satisfaction problem is NP-complete, or the constraint satisfaction problem for $A$ is in P. To prove our result, we study the first-order reducts of the Johnson graph $J(k)$, for $k \geq 2$, whose automorphism group $G$...

arXiv CS 1d ago

Aspects of Coherence in Dependence Logic

arXiv:2605.31269v1 Announce Type: new Abstract: Dependence logic extends first-order logic with dependence atoms asserting that the value of a variable is determined by the values of certain other variables. The semantics of dependence logic has a second-order character and involves sets of assignments, called teams, instead of individual assignments as in the classical Tarski semantics. Since the model-checking problem is known to be NP-complete even for quantifier-free dependence logic...

arXiv CS 9d ago

Word-Representable Co-Bipartite Graphs: Vertex Ordering, Representation Number, Speed, and Entropy

arXiv:2509.03064v2 Announce Type: replace-cross Abstract: A graph $G(V, E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that for distinct letters $x,y\in V$, $x$ and $y$ alternate in $w$ if and only if they are adjacent in $G$. In general, determining whether a graph is word-representable is an NP-complete problem. A graph is co-bipartite if its complement is bipartite. Therefore, the vertex set of a co-bipartite graph can be partitioned into two disjoint...

arXiv CS 7d ago

Terminal Steiner tree problem : Complexity and Algorithms

arXiv:2606.02325v1 Announce Type: new Abstract: Given a connected graph $G$ and a terminal set $R \subseteq V(G)$, the Steiner tree problem (ST) asks for a tree that spans all of $R$ with at most $r$ vertices from $V(G)\backslash R$, for some integer $r\geq 0$. It is known from (Garey et al.,1977 ) that ST is NP-complete.

arXiv CS 8d ago

Tree Containment Parameterized by Scanwidth

arXiv:2605.31071v2 Announce Type: replace Abstract: TREE CONTAINMENT is a central decision problem in mathematical phylogenetics, asking whether a given rooted phylogenetic tree is embeddable in ("displayed by") a given rooted phylogenetic network. While the problem is NP-complete for general networks, many algorithmic advances have relied on structural parameters that capture how "tree-like" a network is. In this paper we investigate TREE CONTAINMENT under the structural parameter...

arXiv CS 2d ago

Odd Cycle Transversal in $P_k$-Free Graphs

arXiv:2606.07453v1 Announce Type: new Abstract: The Odd Cycle Transversal (OCT) problem, which asks for a minimum subset of vertices whose removal renders a graph bipartite, is a central problem in algorithmic graph theory. It is known to be NP-complete even on $P_k$-free graphs for $k \ge 6$. Furthermore, assuming the Unique Games Conjecture (UGC), OCT does not admit a constant-factor approximation algorithm on general graphs.

arXiv CS 2d ago

Removing bottlenecks in the recognition of small $(k,\ell)$-graph classes

arXiv:2510.17665v2 Announce Type: replace Abstract: A graph is a $(k,\ell)$-graph if its vertex set can be partitioned into $k$ independent sets and $\ell$ cliques. This family simultaneously generalizes split, bipartite, and co-bipartite graphs. While the recognition problem is NP-complete whenever $k\geq 3$ or $\ell\geq 3$, the remaining small cases are polynomial-time solvable.

arXiv CS 9d ago

Tree Containment Parameterized by Scanwidth

Announce Type: new Abstract: TREE CONTAINMENT is a central decision problem in mathematical phylogenetics, asking whether a given rooted phylogenetic tree is embeddable in ("displayed by") a given rooted phylogenetic network. While the problem is NP-complete for general networks, many algorithmic advances have relied on structural parameters that capture how "tree-like" a network is. In this paper we investigate TREE CONTAINMENT under the structural parameter scanwidth, a directed width...

arXiv CS 9d ago

Polynomial-time satisfiability for a special case of Positive$\wedge$Negative

Announce Type: new Abstract: A Boolean function in CNF format is of type Positive$\wedge$Negative} if each clause C is either positive (i.e. all literals of C are positive) or negative (i.e. all literals of C are negative). As is well known, deciding the satisfiability of such CNFs is NP-complete. We say that a CNF is of type DisjointPositive if its clauses are positive and mutually disjoint.

arXiv CS 5d ago

End-to-End Subgraph Detection with GraphDETR

Announce Type: new Abstract: Subgraph detection seeks to identify whether and where instances of query patterns occur within a larger graph. This problem is fundamental across scientific domains and is closely related to subgraph isomorphism, which is NP-complete, limiting combinatorial approaches to small patterns or moderately sized graphs. We introduce GraphDETR, a deep learning framework that formulates subgraph detection as a set prediction problem, analogous to DETR in object detection.

arXiv CS 5d ago