arXiv subjects

Petros Petsinis

Publications and source records attributed to Petros Petsinis.

4 recordsLinked to original sources

arXiv2024

Robust Reward Placement under Uncertainty

We consider a problem of placing generators of rewards to be collected by randomly moving agents in a network. In many settings, the precise mobility pattern may be one of several possible, based on parameters outside our control, such as weather conditions. The placement should be robust to this uncertainty, to gain a competent total reward across possible networks. To study such scenarios, we introduce the Robust Reward Placement problem (RRP). Agents move randomly by a Markovian Mobility Model with a predetermined set of locations whose connectivity is chosen adversarially from a known set $Π$ of candidates. We aim to select a set of reward states within a budget that maximizes the minimum ratio, among all candidates in $Π$, of the collected total reward over the optimal collectable reward under the same candidate. We prove that RRP is NP-hard and inapproximable, and develop $Ψ$-Saturate, a pseudo-polynomial time algorithm that achieves an $ε$-additive approximation by exceeding the budget constraint by a factor that scales as $O(\ln |Π|/ε)$. In addition, we present several heuristics, most prominently one inspired by a dynamic programming algorithm for the max-min 0-1 KNAPSACK problem. We corroborate our theoretical analysis with an experimental evaluation on synthetic and real data.

cs.MA↗

arXiv2024

Seed Selection in the Heterogeneous Moran Process

The Moran process is a classic stochastic process that models the rise and takeover of novel traits in network-structured populations. In biological terms, a set of mutants, each with fitness $m\in(0,\infty)$ invade a population of residents with fitness $1$. Each agent reproduces at a rate proportional to its fitness and each offspring replaces a random network neighbor. The process ends when the mutants either fixate (take over the whole population) or go extinct. The fixation probability measures the success of the invasion. To account for environmental heterogeneity, we study a generalization of the Standard process, called the Heterogeneous Moran process. Here, the fitness of each agent is determined both by its type (resident/mutant) and the node it occupies. We study the natural optimization problem of seed selection: given a budget $k$, which $k$ agents should initiate the mutant invasion to maximize the fixation probability? We show that the problem is strongly inapproximable: it is $\mathbf{NP}$-hard to distinguish between maximum fixation probability 0 and 1. We then focus on mutant-biased networks, where each node exhibits at least as large mutant fitness as resident fitness. We show that the problem remains $\mathbf{NP}$-hard, but the fixation probability becomes submodular, and thus the optimization problem admits a greedy $(1-1/e)$-approximation. An experimental evaluation of the greedy algorithm along with various heuristics on real-world data sets corroborates our results.

cs.DS↗

arXiv2023

Maximizing the Probability of Fixation in the Positional Voter Model

The Voter model is a well-studied stochastic process that models the invasion of a novel trait $A$ (e.g., a new opinion, social meme, genetic mutation, magnetic spin) in a network of individuals (agents, people, genes, particles) carrying an existing resident trait $B$. Individuals change traits by occasionally sampling the trait of a neighbor, while an invasion bias $δ\geq 0$ expresses the stochastic preference to adopt the novel trait $A$ over the resident trait $B$. The strength of an invasion is measured by the probability that eventually the whole population adopts trait $A$, i.e., the fixation probability. In more realistic settings, however, the invasion bias is not ubiquitous, but rather manifested only in parts of the network. For instance, when modeling the spread of a social trait, the invasion bias represents localized incentives. In this paper, we generalize the standard biased Voter model to the positional Voter model, in which the invasion bias is effectuated only on an arbitrary subset of the network nodes, called biased nodes. We study the ensuing optimization problem, which is, given a budget $k$, to choose $k$ biased nodes so as to maximize the fixation probability of a randomly occurring invasion. We show that the problem is NP-hard both for finite $δ$ and when $δ\rightarrow \infty$ (strong bias), while the objective function is not submodular in either setting, indicating strong computational hardness. On the other hand, we show that, when $δ\rightarrow 0$ (weak bias), we can obtain a tight approximation in $O(n^{2ω})$ time, where $ω$ is the matrix-multiplication exponent. We complement our theoretical results with an experimental evaluation of some proposed heuristics.

q-bio.PE↗

arXiv2021

Analysis of key flavors of event-driven predictive maintenance using logs of phenomena described by Weibull distributions

This work explores two approaches to event-driven predictive maintenance in Industry 4.0 that cast the problem at hand as a classification or a regression one, respectively, using as a starting point two state-of-the-art solutions. For each of the two approaches, we examine different data preprocessing techniques, different prediction algorithms and the impact of ensemble and sampling methods. Through systematic experiments regarding the aspectsmentioned above,we aimto understand the strengths of the alternatives, and more importantly, shed light on how to navigate through the vast number of such alternatives in an informed manner. Our work constitutes a key step towards understanding the true potential of this type of data-driven predictive maintenance as of to date, and assist practitioners in focusing on the aspects that have the greatest impact.

cs.LG↗