Related papers: A Combinatorial Approximation Algorithm for Graph …
We consider the following special case of minimizing makespan. A set of jobs $J$ and a set of machines $M$ are given. Each job $j \in J$ can be scheduled on a machine from a subset $M_j$ of $M$. The processing time of $j$ is the same on all…
Minimum Weight Cycle (MWC) is the problem of finding a simple cycle of minimum weight in a graph $G=(V,E)$. This is a fundamental graph problem with classical sequential algorithms that run in $\tilde{O}(n^3)$ and $\tilde{O}(mn)$ time where…
Jaberi [7] presented approximation algorithms for the problem of computing a minimum size 2-vertex strongly biconnected subgraph in directed graphs. We have implemented approximation algorithms presented in [7] and we have tested the…
We are given a set of $n$ jobs that have to be executed on a set of $m$ speed-scalable machines that can vary their speeds dynamically using the energy model introduced in [Yao et al., FOCS'95]. Every job $j$ is characterized by its release…
Finding schedules for pairwise meetings between the members of a complex social group without creating interpersonal conflict is challenging, especially when different relationships have different needs. We formally define and study the…
Optimization problems consist of either maximizing or minimizing an objective function. Instead of looking for a maximum solution (resp. minimum solution), one can find a minimum maximal solution (resp. maximum minimal solution). Such…
We study the multi-task linear regression problem in the presence of contaminated tasks. We address the setting where the unknown parameters of a majority of tasks are close in the $\ell_2$-norm, while a fraction of tasks are arbitrary…
In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…
This article is devoted to propose some lower and upper bounds for the coupled-tasks scheduling problem in presence of compatibility constraints according to classical complexity hypothesis ($\mathcal{P} \neq \mathcal{NP}$,…
Many complex systems and datasets are characterized by multiway interactions of different categories, and can be modeled as edge-colored hypergraphs. We focus on clustering such datasets using the NP-hard edge-colored clustering problem,…
This paper presents a fast and simple new 2-approximation algorithm for minimum weighted vertex cover. The unweighted version of this algorithm is equivalent to a well-known greedy maximal independent set algorithm. We prove that this…
Makespan minimization on identical parallel machines is a classical scheduling problem. We consider the online scenario where a sequence of $n$ jobs has to be scheduled non-preemptively on $m$ machines so as to minimize the maximum…
We design new deterministic CONGEST approximation algorithms for \emph{maximum weight independent set (MWIS)} in \emph{sparse graphs}. As our main results, we obtain new $\Delta(1+\epsilon)$-approximation algorithms as well as algorithms…
We revisit two well-studied scheduling problems in the unrelated machines setting where each job can have a different processing time on each machine. For minimizing total weighted completion time we give a 1.45-approximation, which…
A large number of applications such as querying sensor networks, and analyzing protein-protein interaction (PPI) networks, rely on mining uncertain graph and hypergraph databases. In this work we study the following problem: given an…
We present a new approximation algorithm for the minimum 2-edge-connected spanning subgraph problem. Its approximation ratio is $\frac{4}{3}$, which matches the current best ratio. The approximation ratio of the algorithm is $\frac{6}{5}$…
Near ubiquitous mobile computing has led to intense interest in dynamic graph theory. This provides a new and challenging setting for algorithmics and complexity theory. For any graph-based problem, the rapid evolution of a (possibly…
We consider the Vector Scheduling problem on identical machines: we have m machines, and a set J of n jobs, where each job j has a processing-time vector $p_j\in \mathbb{R}^d_{\geq 0}$. The goal is to find an assignment $\sigma:J\to [m]$ of…
For any $\varepsilon > 0$, we give a polynomial-time $n^\varepsilon$-approximation algorithm for Max Independent Set in graphs of bounded twin-width given with an $O(1)$-sequence. This result is derived from the following time-approximation…
There is a long history of approximation schemes for the problem of scheduling jobs on identical machines to minimize the makespan. Such a scheme grants a $(1+\epsilon)$-approximation solution for every $\epsilon > 0$, but the running time…