Related papers: A Polynomial Time Solution to the Clique Problem
Temporal graphs have been recently introduced to model changes to a given network that occur throughout a fixed period of time. The Temporal $\Delta$ Clique problem, that generalizes the well known Clique problem to temporal graphs, has…
We study the problem of approximating the number of $k$-cliques in a graph when given query access to the graph. We consider the standard query model for general graphs via (1) degree queries, (2) neighbor queries and (3) pair queries. Let…
A graph G is prismatic if for every triangle T of G, every vertex of G not in T has a unique neighbour in T. The complement of a prismatic graph is called \emph{antiprismatic}. The complexity of colouring antiprismatic graphs is still…
The $k$-Maximum Dispersion Problem with Cardinality Constraints ($k$-MDCC) asks for a partition of a given item set with pairwise dissimilarities into $k$ cardinality-constrained groups such that the minimum pairwise intra-group…
We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first,…
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…
We propose an unsupervised approach for learning vertex orderings for the maximum clique problem by framing it within a permutation-based framework. We transform the combinatorial constraints into geometric relationships such that the…
Lattice reduction algorithms have numerous applications in number theory, algebra, as well as in cryptanalysis. The most famous algorithm for lattice reduction is the LLL algorithm. In polynomial time it computes a reduced basis with…
The generic homomorphism problem, which asks whether an input graph $G$ admits a homomorphism into a fixed target graph $H$, has been widely studied in the literature. In this article, we provide a fine-grained complexity classification of…
The aim of power management policies is to reduce the amount of energy consumed by computer systems while maintaining satisfactory level of performance. One common method for saving energy is to simply suspend the system during the idle…
The CFG recognition problem is: given a context-free grammar $\mathcal{G}$ and a string $w$ of length $n$, decide if $w$ can be obtained from $\mathcal{G}$. This is the most basic parsing question and is a core computer science problem.…
This contribution extends the Bron Kerbosch algorithm for solving the maximum weight clique problem, where continuous-valued weights are assigned to both, vertices and edges. We applied the proposed algorithm to graph matching problems.
Link streams model interactions over time, and a clique in a link stream is defined as a set of nodes and a time interval such that all pairs of nodes in this set interact permanently during this time interval. This notion was introduced…
The {Congested Clique} is a distributed-computing model for single-hop networks with restricted bandwidth that has been very intensively studied recently. It models a network by an $n$-vertex graph in which any pair of vertices can…
We consider the maintenance of the set of all maximal cliques in a dynamic graph that is changing through the addition or deletion of edges. We present nearly tight bounds on the magnitude of change in the set of maximal cliques, as well as…
It is known that the maximum cardinality cut problem is NP-hard even in chordal graphs. In this paper, we consider the time complexity of the problem in proper interval graphs, a subclass of chordal graphs, and propose a dynamic programming…
Many problems of interest for cyber-physical network systems can be formulated as Mixed Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class…
It is shown that graph-theoretic problem CLIQUE can't be solved in polynomial time by any deterministic TM. This upgrades the well-known partial result that claims only monotone unsolvability thereof, and eventually implies P $\neq$ NP as…
I introduce a new approach to the maximum flow problem by a simple algorithm with a slightly better runtime. This approach is based on sorting arcs insight of vertices on a residual graph. This new approach leads to an O(mn^0.5) time bound…
A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for \textsc{Maximum Clique} on unit disk graphs [Clark, Colbourn, Johnson; Discrete…