Related papers: A Polynomial Time Solution to the Clique Problem
In this work we consider the problem of maximizing the PageRank of a given target node in a graph by adding $k$ new links. We consider the case that the new links must point to the given target node (backlinks). Previous work shows that…
We complete the complexity classification by degree of minimizing a polynomial over the integer points in a polyhedron in $\mathbb{R}^2$. Previous work shows that optimizing a quadratic polynomial over the integer points in a polyhedral…
We present a new formulation of the maximum clique problem of a graph in complex space. We start observing that the adjacency matrix A of a graph can always be written in the form A = B B where B is a complex, symmetric matrix formed by…
The maximal clique enumeration (MCE) problem has numerous applications in biology, chemistry, sociology, and graph modeling. Though this problem is well studied, most current research focuses on finding solutions in large sparse graphs or…
Finding cliques in a graph has several applications for its pattern matching ability. $k$-clique problem, a special case of clique problem, determines whether an arbitrary graph contains a clique of size $k$, has already been addressed in…
The maximum clique problem finds applications in computer vision, bioinformatics, and network analysis, many of which involve the construction of correspondence graphs to find similarities between two given objects. cliquematch is a Python…
In the EDGE CLIQUE COVER (ECC) problem, given a graph G and an integer k, we ask whether the edges of G can be covered with k complete subgraphs of G or, equivalently, whether G admits an intersection model on k-element universe. Gramm et…
The main results of this paper are (I) a simulation algorithm which, under quite general constraints, transforms algorithms running on the Congested Clique into algorithms running in the MapReduce model, and (II) a distributed…
We provide faster strongly polynomial time algorithms solving maximum flow in structured $n$-node $m$-arc networks. Our results imply an $n^{\omega + o(1)}$-time strongly polynomial time algorithms for computing a maximum bipartite…
In this paper, we address the minimum-cost node-capacitated multiflow problem in an undirected network. For this problem, Babenko and Karzanov (2012) showed strongly polynomial-time solvability via the ellipsoid method. Our result is the…
Ray intersection graphs are intersection graphs of rays, or halflines, in the plane. We show that any planar graph has an even subdivision whose complement is a ray intersection graph. The construction can be done in polynomial time and…
We study the possibility of designing $N^{o(1)}$-round protocols for problems of substantially super-linear polynomial-time (sequential) complexity on the congested clique with about $N^{1/2}$ nodes, where $N$ is the input size. We show…
A graph is inductive $k$-independent if there exists and ordering of its vertices $v_{1},...,v_{n}$ such that $\alpha(G[N(v_{i})\cap V_{i}])\leq k $ where $N(v_{i})$ is the neighborhood of $v_{i}$, $V_{i}=\{v_{i},...,v_{n}\}$ and $\alpha$…
In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a…
In the 90's Clark, Colbourn and Johnson wrote a seminal paper where they proved that maximum clique can be solved in polynomial time in unit disk graphs. Since then, the complexity of maximum clique in intersection graphs of d-dimensional…
Chordal decomposition techniques are used to reduce large structured positive semidefinite matrix constraints in semidefinite programs (SDPs). The resulting equivalent problem contains multiple smaller constraints on the nonzero blocks (or…
A set of vertices in a graph forms a potential maximal clique if there exists a minimal chordal completion in which it is a maximal clique. Potential maximal cliques were first introduced as a key tool to obtain an efficient, though…
Given a set $P$ of $n$ points in the plane, the unit-disk graph $G(P)$ is a graph with $P$ as its vertex set such that two points of $P$ have an edge if their Euclidean distance is at most $1$. We consider the problem of computing a maximum…
The planted clique problem is well-studied in the context of observing, explaining, and predicting interesting computational phenomena associated with statistical problems. When equating computational efficiency with the existence of…
The Maximum Flow Problem with Conflict Constraints is a generalization that adds conflict constraints to a classical optimization problem on networks used to model several real-world applications. In the last few years several approaches,…