arXiv subjects

Esmaeil Delfaraz

Publications and source records attributed to Esmaeil Delfaraz.

6 recordsLinked to original sources

arXiv2025

An Approximation Algorithm for the Connected Maximum Coverage Problem in Directed Graphs

In the Directed rooted Connected Budgeted maximum Coverage problem (\DRCC), we are given a collection of subsets $\mathcal{S}$, defined over a ground set $X$, and a directed graph $G=(V,E)$, where each node is associated with a set of $\mathcal{S}$. Each set in $\mathcal{S}$ has a different cost and each element of $X$ gives a different prize. The goal is to find a subcollection $\mathcal{S}'\subseteq \mathcal{S}$ such that $\mathcal{S}'$ induces an out-tree rooted at a given node, the total cost of the sets in $\mathcal{S}'$ does not exceed a budget $B$, and the total prize of the elements covered by $\mathcal{S}'$ is maximized. In this paper, we provide an algorithm for \DRCC that guarantees an approximation ratio of $O\left(\frac{\sqrt{|V|}\log^2|X|}{\epsilon^2}\right)$, with a budget violation of a factor $1+\epsilon$, where $\epsilon\in (0,1]$. Our algorithm also implies an improved approximation factor for the budgeted node-weighted Steiner problem in directed graphs, a particular case of \DRCC where the prize function is additive, for which we improve from $O\left(\frac{1}{\epsilon^2}|V|^{2/3}\log|V|\right)$ to $O\left(\frac{1}{\epsilon^2}|V|^{1/2}\log^2|V|\right)$.

cs.DS↗

arXiv2022

Approximation algorithms for Node-weighted Steiner Problems: Digraphs with Additive Prizes and Graphs with Submodular Prizes

In the \emph{budgeted rooted node-weighted Steiner tree} problem, we are given a graph $G$ with $n$ nodes, a predefined node $r$, two weights associated to each node modelling costs and prizes. The aim is to find a tree in $G$ rooted at $r$ such that the total cost of its nodes is at most a given budget $B$ and the total prize is maximized. In the \emph{quota rooted node-weighted Steiner tree} problem, we are given a real-valued quota $Q$, instead of the budget, and we aim at minimizing the cost of a tree rooted at $r$ whose overall prize is at least $Q$. For the case of directed graphs with additive prize function, we develop a technique resorting on a standard flow-based linear programming relaxation to compute a tree with good trade-off between prize and cost, which allows us to provide very simple polynomial time approximation algorithms for both the budgeted and the quota problems. For the \emph{budgeted} problem, our algorithm achieves a bicriteria $(1+ε, O(\frac{1}{ε^2}n^{2/3}\ln{n}))$-approximation, for any $ε\in (0, 1]$. For the \emph{quota} problem, our algorithm guarantees a bicriteria approximation factor of $(2, O(n^{2/3}\ln{n}))$. Next, by using the flow-based LP, we provide a surprisingly simple polynomial time $O((1+ε)\sqrt{n} \ln {n})$-approximation algorithm for the node-weighted version of the directed Steiner tree problem, for any $ε>0$. For the case of undirected graphs with monotone submodular prize functions over subsets of nodes, we provide a polynomial time $O(\frac{1}{ε^3}\sqrt{n}\log{n})$-approximation algorithm for the budgeted problem that violates the budget constraint by a factor of at most $1+ε$, for any $ε\in (0, 1]$. Our technique allows us to provide a good approximation also for the quota problem.

cs.DS↗

arXiv2022

Budgeted Out-tree Maximization with Submodular Prizes

We consider a variant of the prize collecting Steiner tree problem in which we are given a \emph{directed graph} $D=(V,A)$, a monotone submodular prize function $p:2^V \rightarrow \mathbb{R}^+ \cup \{0\}$, a cost function $c:V \rightarrow \mathbb{Z}^{+}$, a root vertex $r \in V$, and a budget $B$. The aim is to find an out-subtree $T$ of $D$ rooted at $r$ that costs at most $B$ and maximizes the prize function. We call this problem \emph{Directed Rooted Submodular Tree} (\textbf{DRSO}). Very recently, Ghuge and Nagarajan [SODA\ 2020] gave an optimal quasi-polynomial-time $O\left(\frac{\log n'}{\log \log n'}\right)$-approximation algorithm, where $n'$ is the number of vertices in an optimal solution, for the case in which the costs are associated to the edges. In this paper, we give a polynomial-time algorithm for \textbf{DRSO} that guarantees an approximation factor of $O(\sqrt{B}/ε^3)$ at the cost of a budget violation of a factor $1+ε$, for any $ε\in (0,1]$. The same result holds for the edge-cost case, to the best of our knowledge this is the first polynomial-time approximation algorithm for this case. We further show that the unrooted version of \textbf{DRSO} can be approximated to a factor of $O(\sqrt{B})$ without budget violation, which is an improvement over the factor $O(Δ\sqrt{B})$ given in~[Kuo et al.\ IEEE/ACM\ Trans.\ Netw.\ 2015] for the undirected and unrooted case, where $Δ$ is the maximum degree of the graph. Finally, we provide some new/improved approximation bounds for several related problems, including the additive-prize version of \textbf{DRSO}, the maximum budgeted connected set cover problem, and the budgeted sensor cover problem.

cs.DS↗

arXiv2022

Computation and Bribery of Voting Power in Delegative Simple Games

Following Zhang and Grossi~(AAAI 2021), we study in more depth a variant of weighted voting games in which agents' weights are induced by a transitive support structure. This class of simple games is notably well suited to study the relative importance of agents in the liquid democracy framework. We first propose a pseudo-polynomial time algorithm to compute the Banzhaf and Shapley-Shubik indices for this class of game. Then, we study a bribery problem, in which one tries to maximize/minimize the voting power/weight of a given agent by changing the support structure under a budget constraint. We show that these problems are computationally hard and provide several parameterized complexity results.

cs.GT↗

arXiv2021

Hole Detection and Healing in Hybrid Sensor Networks

Although monitoring and covering are fundamental goals of a wireless sensor network (WSN), the accidental death of sensors or the running out of their energy would result in holes in the WSN. Such holes have the potential to disrupt the primary functions of WSNs. This paper investigates the hole detection and healing problems in hybrid WSNs with non-identical sensor sensing ranges. In particular, we aim to propose centralized algorithms for detecting holes in a given region and maximizing the area covered by a WSN in the presence of environmental obstacles. To precisely identify the boundary of the holes, we use an additively weighted Voronoi diagram and a polynomial-time algorithm.Furthermore, since this problem is known to be computationally difficult, we propose a centralized greedy 1/2-approximation algorithm to maximize the area covered by sensors. Finally, we implement the algorithms and run simulations to show that our approximation algorithm efficiently covers the holes by moving the mobile sensors.

cs.CG↗

arXiv2021

When Can Liquid Democracy Unveil the Truth?

In this paper, we investigate the so-called ODP-problem that has been formulated by Caragiannis and Micha [10]. Here, we are in a setting with two election alternatives out of which one is assumed to be correct. In ODP, the goal is to organise the delegations in the social network in order to maximize the probability that the correct alternative, referred to as ground truth, is elected. While the problem is known to be computationally hard, we strengthen existing hardness results by providing a novel strong approximation hardness result: For any positive constant $C$, we prove that, unless $P=NP$, there is no polynomial-time algorithm for ODP that achieves an approximation guarantee of $α\ge (\ln n)^{-C}$, where $n$ is the number of voters. The reduction designed for this result uses poorly connected social networks in which some voters suffer from misinformation. Interestingly, under some hypothesis on either the accuracies of voters or the connectivity of the network, we obtain a polynomial-time $1/2$-approximation algorithm. This observation proves formally that the connectivity of the social network is a key feature for the efficiency of the liquid democracy paradigm. Lastly, we run extensive simulations and observe that simple algorithms (working either in a centralized or decentralized way) outperform direct democracy on a large class of instances. Overall, our contributions yield new insights on the question in which situations liquid democracy can be beneficial.

cs.GT↗