Related papers: Maximum $k$-Plex Search: An Alternated Reduction-a…
The max-k-cut problem is to partition the vertices of a weighted graph $G = (V,E)$ into $k\geq2$ disjoint subsets such that the weight sum of the edges crossing the different subsets is maximized. The problem is referred as the max-cut…
Bipartite graphs are a prevalent modeling tool for real-world networks, capturing interactions between vertices of two different types. Within this framework, bicliques emerge as crucial structures when studying dense subgraphs: they are…
We introduce a search problem for finding a regular bi-partite graph of maximum attainable girth for specified degree and number of vertices, by restricting the search space using a series of mathematically rigourous arguments from [1] and…
In this paper, we present a Branch and Bound algorithm called QuickBB for computing the treewidth of an undirected graph. This algorithm performs a search in the space of perfect elimination ordering of vertices of the graph. The algorithm…
Combinatorial branch and bound searches are a common technique for solving global optimisation and decision problems. Their performance often depends on good search order heuristics, refined over decades of algorithms research. Parallel…
There has been a rise in the popularity of algebraic methods for graph algorithms given the development of the GraphBLAS library and other sparse matrix methods. An exemplar for these approaches is Breadth-First Search (BFS). The algebraic…
We propose a fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks. The method exhibits a roughly linear runtime scaling over real-world networks…
Nonconvex optimization refers to the process of solving problems whose objective or constraints are nonconvex. Historically, this type of problems have been very difficult to solve to global optimality, with traditional solvers often…
Branch-and-bound is a systematic enumerative method for combinatorial optimization, where the performance highly relies on the variable selection strategy. State-of-the-art handcrafted heuristic strategies suffer from relatively slow…
The series-parallel (active) redundancy allocation problem with mixed components (RAP) involves setting reliable objectives for components or subsystems to meet the resource consumption constraint, e.g., the total cost. RAP has been an…
We study the maximum $k$-colorable subgraph (M$k$CS) problem, which consists in finding a largest $k$-colorable induced subgraph in a given graph. We consider a Semidefinite Programming (SDP) relaxation for the M$k$CS problem and regard its…
$k$-defective cliques relax cliques by allowing up-to $k$ missing edges from being a complete graph. This relaxation enables us to find larger near-cliques and has applications in link prediction, cluster detection, social network analysis…
The maximum k-plex problem is a computationally complex problem, which emerged from graph-theoretic social network studies. This paper presents an effective hybrid local search for solving the maximum k-plex problem that combines the…
We introduce a novel method for clustering using a semidefinite programming (SDP) relaxation of the Max k-Cut problem. The approach is based on a new methodology for rounding the solution of an SDP relaxation using iterated linear…
One of the challenges of cloud computing is to optimally and efficiently assign virtual ma- chines to physical machines. The aim of telecommunication operators is to minimize the map- ping cost while respecting constraints regarding…
Akiba and Iwata [TCS, 2016] demonstrated that a branch and reduce (B&R) solver for the vertex cover problem can compete favorably with integer linear programming solvers (e.g., CPLEX). Our research question is are there graph…
The Max-k-Cut problem is a fundamental combinatorial optimization challenge that generalizes the classic NP-complete Max-Cut problem. While relaxation techniques are commonly employed to tackle Max-k-Cut, they often lack guarantees of…
In a network, a $k$-plex represents a subset of $n$ vertices where the degree of each vertex in the subnetwork induced by this subset is at least $n-k$. The maximum edge-weight $k$-plex partitioning problem (Max-EkPP) is to find the…
SPARQL basic graph pattern (BGP) (a.k.a. SQL inner-join) query optimization is a well researched area. However, optimization of OPTIONAL pattern queries (a.k.a. SQL left-outer-joins) poses additional challenges, due to the restrictions on…
Many fixed-parameter tractable algorithms using a bounded search tree have been repeatedly improved, often by describing a larger number of branching rules involving an increasingly complex case analysis. We introduce a novel and general…