Related papers: Minimum-weight partitioning of a set with associat…
The paper describes a simple deterministic parallel/distributed (2+epsilon)-approximation algorithm for the minimum-weight vertex-cover problem and its dual (edge/element packing).
In this paper we study a max-min $k$-partition problem on a weighted graph, that could model a robust $k$-coalition formation. We settle the computational complexity of this problem as complete for class $\Sigma_2^P$. This hardness holds…
Approximating Subset Sum is a classic and fundamental problem in computer science and mathematical optimization. The state-of-the-art approximation scheme for Subset Sum computes a $(1-\varepsilon)$-approximation in time…
A scalable graphical method is presented for selecting, and partitioning datasets for the training phase of a classification task. For the heuristic, a clustering algorithm is required to get its computation cost in a reasonable proportion…
This paper presents a new combinatorial optimisation task, the Subset Sum Matching Problem (SSMP), which is an abstraction of common financial applications such as trades reconciliation. We present three algorithms, two suboptimal and one…
We consider a parallel system of $m$ identical machines prone to unpredictable crashes and restarts, trying to cope with the continuous arrival of tasks to be executed. Tasks have different computational requirements (i.e., processing time…
We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks,…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems.…
Bipartite Correlation clustering is the problem of generating a set of disjoint bi-cliques on a set of nodes while minimizing the symmetric difference to a bipartite input graph. The number or size of the output clusters is not constrained…
We study a natural variant of scheduling that we call \emph{partial scheduling}: In this variant an instance of a scheduling problem along with an integer $k$ is given and one seeks an optimal schedule where not all, but only $k$ jobs, have…
In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate…
Parameterized complexity theory offers a framework for a refined analysis of hard algorithmic problems. Instead of expressing the running time of an algorithm as a function of the input size only, running times are expressed with respect to…
For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a…
The benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem. The performance of this new method, called Extremal Optimization, is compared to Simulated Annealing in…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…
Many scenarios where agents with restrictions compete for resources can be cast as maximum matching problems on bipartite graphs. Our focus is on resource allocation problems where agents may have restrictions that make them incompatible…
A mixed dominating set of a graph $G = (V, E)$ is a mixed set $D$ of vertices and edges, such that for every edge or vertex, if it is not in $D$, then it is adjacent or incident to at least one vertex or edge in $D$. The mixed domination…
Let $n > m\ge 2$ be integers and let $\mathcal{A}=\{A_1,\dots,A_m\}$ be a partition of $[n]=\{1,\dots,n\}$. For $X \subseteq [n]$, its $\mathcal{A}$-boundary region $\mathcal{A}(X)$ is defined to be the union of those blocks $A_i$ of…