arXiv subjects

Vincenzo Bonifaci

Publications and source records attributed to Vincenzo Bonifaci.

12 recordsLinked to original sources

arXiv2024

On a Voter Model with Context-Dependent Opinion Adoption

Opinion diffusion is a crucial phenomenon in social networks, often underlying the way in which a collective of agents develops a consensus on relevant decisions. The voter model is a well-known theoretical model to study opinion spreading in social networks and structured populations. Its simplest version assumes that an updating agent will adopt the opinion of a neighboring agent chosen at random. The model allows us to study, for example, the probability that a certain opinion will fixate into a consensus opinion, as well as the expected time it takes for a consensus opinion to emerge. Standard voter models are oblivious to the opinions held by the agents involved in the opinion adoption process. We propose and study a context-dependent opinion spreading process on an arbitrary social graph, in which the probability that an agent abandons opinion $a$ in favor of opinion $b$ depends on both $a$ and $b$. We discuss the relations of the model with existing voter models and then derive theoretical results for both the fixation probability and the expected consensus time for two opinions, for both the synchronous and the asynchronous update models.

cs.MA↗

arXiv2022

Physarum-Inspired Multi-Commodity Flow Dynamics

In wet-lab experiments, the slime mold Physarum polycephalum has demonstrated its ability to solve shortest path problems and to design efficient networks. For the shortest path problem, a mathematical model for the evolution of the slime is available and it has been shown in computer experiments and through mathematical analysis that the dynamics solves the shortest path problem. In this paper, we introduce a dynamics for the network design problem. We formulate network design as the problem of constructing a network that efficiently supports a multi-commodity flow problem. We investigate the dynamics in computer simulations and analytically. The simulations show that the dynamics is able to construct efficient and elegant networks. In the theoretical part we show that the dynamics minimizes an objective combining the cost of the network and the cost of routing the demands through the network. We also give alternative characterization of the optimum solution.

cs.DS↗

arXiv2019

A Laplacian Approach to $\ell_1$-Norm Minimization

We propose a novel differentiable reformulation of the linearly-constrained $\ell_1$ minimization problem, also known as the basis pursuit problem. The reformulation is inspired by the Laplacian paradigm of network theory and leads to a new family of gradient-based methods for the solution of $\ell_1$ minimization problems. We analyze the iteration complexity of a natural solution approach to the reformulation, based on a multiplicative weights update scheme, as well as the iteration complexity of an accelerated gradient scheme. The results can be seen as bounds on the complexity of iteratively reweighted least squares (IRLS) type methods of basis pursuit.

cs.DS↗

arXiv2018

Two Results on Slime Mold Computations

We present two results on slime mold computations. In wet-lab experiments (Nature'00) by Nakagaki et al. the slime mold Physarum polycephalum demonstrated its ability to solve shortest path problems. Biologists proposed a mathematical model, a system of differential equations, for the slime's adaption process (J. Theoretical Biology'07). It was shown that the process convergences to the shortest path (J. Theoretical Biology'12) for all graphs. We show that the dynamics actually converges for a much wider class of problems, namely undirected linear programs with a non-negative cost vector. Combinatorial optimization researchers took the dynamics describing slime behavior as an inspiration for an optimization method and showed that its discretization can $\varepsilon$-approximately solve linear programs with positive cost vector (ITCS'16). Their analysis requires a feasible starting point, a step size depending linearly on $\varepsilon$, and a number of steps with quartic dependence on $\mathrm{opt}/(\varepsilonΦ)$, where $Φ$ is the difference between the smallest cost of a non-optimal basic feasible solution and the optimal cost ($\mathrm{opt}$). We give a refined analysis showing that the dynamics initialized with any strongly dominating point converges to the set of optimal solutions. Moreover, we strengthen the convergence rate bounds and prove that the step size is independent of $\varepsilon$, and the number of steps depends logarithmically on $1/\varepsilon$ and quadratically on $\mathrm{opt}/Φ$.

cs.DS↗

arXiv2018

Pooling or Sampling: Collective Dynamics for Electrical Flow Estimation

The computation of electrical flows is a crucial primitive for many recently proposed optimization algorithms on weighted networks. While typically implemented as a centralized subroutine, the ability to perform this task in a fully decentralized way is implicit in a number of biological systems. Thus, a natural question is whether this task can provably be accomplished in an efficient way by a network of agents executing a simple protocol. We provide a positive answer, proposing two distributed approaches to electrical flow computation on a weighted network: a deterministic process mimicking Jacobi's iterative method for solving linear systems, and a randomized token diffusion process, based on revisiting a classical random walk process on a graph with an absorbing node. We show that both processes converge to a solution of Kirchhoff's node potential equations, derive bounds on their convergence rates in terms of the weights of the network, and analyze their time and message complexity.

cs.DC↗

arXiv2016

On the Convergence Time of a Natural Dynamics for Linear Programming

We consider a system of nonlinear ordinary differential equations for the solution of linear programming (LP) problems that was first proposed in the mathematical biology literature as a model for the foraging behavior of acellular slime mold Physarum polycephalum, and more recently considered as a method to solve LPs. We study the convergence time of the continuous Physarum dynamics in the context of the linear programming problem, and derive a new time bound to approximate optimality that depends on the relative entropy between projected versions of the optimal point and of the initial point. The bound scales logarithmically with the LP cost coefficients and linearly with the inverse of the relative accuracy, establishing the efficiency of the dynamics for arbitrary LP instances with positive costs.

math.OC↗

arXiv2016

A revised model of fluid transport optimization in Physarum polycephalum

Optimization of fluid transport in the slime mold Physarum polycephalum has been the subject of several modeling efforts in recent literature. Existing models assume that the tube adaptation mechanism in P. polycephalum's tubular network is controlled by the sheer amount of fluid flow through the tubes. We put forward the hypothesis that the controlling variable may instead be the flow's pressure gradient along the tube. We carry out the stability analysis of such a revised mathematical model for a parallel-edge network, proving that the revised model supports the global flow-optimizing behavior of the slime mold for a substantially wider class of response functions compared to previous models. Simulations also suggest that the same conclusion may be valid for arbitrary network topologies.

q-bio.TO↗

arXiv2012

Feasibility Tests for Recurrent Real-Time Tasks in the Sporadic DAG Model

A model has been proposed in [Baruah et al., in Proceedings of the IEEE Real-Time Systems Symposium 2012] for representing recurrent precedence-constrained tasks to be executed on multiprocessor platforms, where each recurrent task is modeled by a directed acyclic graph (DAG), a period, and a relative deadline. Each vertex of the DAG represents a sequential job, while the edges of the DAG represent precedence constraints between these jobs. All the jobs of the DAG are released simultaneously and have to be completed within some specified relative deadline. The task may release jobs in this manner an unbounded number of times, with successive releases occurring at least the specified period apart. The feasibility problem is to determine whether such a recurrent task can be scheduled to always meet all deadlines on a specified number of dedicated processors. The case of a single task has been considered in [Baruah et al., 2012]. The main contribution of this paper is to consider the case of multiple tasks. We show that EDF has a speedup bound of 2-1/m, where m is the number of processors. Moreover, we present polynomial and pseudopolynomial schedulability tests, of differing effectiveness, for determining whether a set of sporadic DAG tasks can be scheduled by EDF to meet all deadlines on a specified number of processors.

cs.DS↗

arXiv2012

Scheduling Unrelated Machines of Few Different Types

A very well-known machine model in scheduling allows the machines to be unrelated, modelling jobs that might have different characteristics on each machine. Due to its generality, many optimization problems of this form are very difficult to tackle and typically APX-hard. However, in many applications the number of different types of machines, such as processor cores, GPUs, etc. is very limited. In this paper, we address this point and study the assignment of jobs to unrelated machines in the case that each machine belongs to one of a fixed number of types and the machines of each type are identical. We present polynomial time approximation schemes (PTASs) for minimizing the makespan for multidimensional jobs with a fixed number of dimensions and for minimizing the L_p-norm. In particular, our results subsume and generalize the existing PTASs for a constant number of unrelated machines and for an arbitrary number of identical machines for these problems. We employ a number of techniques which go beyond the previously known results, including a new counting argument and a method for making the concept of sparse extreme point solutions usable for a convex program.

cs.DS↗

arXiv2011

Physarum Can Compute Shortest Paths

Physarum Polycephalum is a slime mold that is apparently able to solve shortest path problems. A mathematical model has been proposed by biologists to describe the feedback mechanism used by the slime mold to adapt its tubular channels while foraging two food sources s0 and s1. We prove that, under this model, the mass of the mold will eventually converge to the shortest s0 - s1 path of the network that the mold lies on, independently of the structure of the network or of the initial mass distribution. This matches the experimental observations by the biologists and can be seen as an example of a "natural algorithm", that is, an algorithm developed by evolution over millions of years.

cs.DS↗

arXiv2010

Feasibility Analysis of Sporadic Real-Time Multiprocessor Task Systems

We give the first algorithm for testing the feasibility of a system of sporadic real-time tasks on a set of identical processors, solving one major open problem in the area of multiprocessor real-time scheduling [S.K. Baruah and K. Pruhs, Journal of Scheduling, 2009]. We also investigate the related notion of schedulability and a notion that we call online feasibility. Finally, we show that discrete-time schedules are as powerful as continuous-time schedules, which answers another open question in the above mentioned survey.

cs.DS↗

arXiv2008

Minimizing Flow Time in the Wireless Gathering Problem

We address the problem of efficient data gathering in a wireless network through multi-hop communication. We focus on the objective of minimizing the maximum flow time of a data packet. We prove that no polynomial time algorithm for this problem can have approximation ratio less than $Ω(m^{1/3)$ when $m$ packets have to be transmitted, unless $P = NP$. We then use resource augmentation to assess the performance of a FIFO-like strategy. We prove that this strategy is 5-speed optimal, i.e., its cost remains within the optimal cost if we allow the algorithm to transmit data at a speed 5 times higher than that of the optimal solution we compare to.

cs.DS↗