arXiv subjects

Faryad Darabi Sahneh

Publications and source records attributed to Faryad Darabi Sahneh.

At least 19 recordsLinked to original sources

arXiv2026

EpidemIQs: Prompt-to-Paper LLM Agents for Epidemic Modeling and Analysis

Large Language Models (LLMs) offer new opportunities to accelerate complex interdisciplinary research domains. Epidemic modeling, characterized by its complexity and reliance on network science, dynamical systems, epidemiology, and stochastic simulations, represents a prime candidate for leveraging LLM-driven automation. We introduce EpidemIQs, a novel multi-agent LLM framework that integrates user inputs and autonomously conducts literature review, analytical derivation, network modeling, mechanistic modeling, stochastic simulations, data visualization and analysis, and finally documentation of findings in a structured manuscript, through five predefined research phases. We introduce two types of agents: a scientist agent for planning, coordination, reflection, and generation of final results, and a task-expert agent to focus exclusively on one specific duty serving as a tool to the scientist agent. The framework consistently generated complete reports in scientific article format. Specifically, using GPT 4.1 and GPT 4.1 Mini as backbone LLMs for scientist and task-expert agents, respectively, the autonomous process completes with average total token usage 870K at a cost of about $1.57 per study, successfully executing all phases and final report. We evaluate EpidemIQs across several different epidemic scenarios, measuring computational cost, workflow reliability, task success rate, and LLM-as-Judge and human expert reviews to estimate the overall quality and technical correctness of the generated results. Through our experiments, the framework consistently addresses evaluation scenarios with an average task success rate of 79%. We compare EpidemIQs to an iterative single-agent LLM, benefiting from the same system prompts and tools, iteratively planning, invoking tools, and revising outputs until task completion. The comparisons suggest a consistently higher performance of EpidemIQs.

cs.SI↗

arXiv2024

FastGEMF: Scalable High-Speed Simulation of Stochastic Spreading Processes over Complex Multilayer Networks

Predicting the spread of processes across complex multi-layered networks has long challenged researchers due to the intricate interplay between network structure and propagation dynamics. Each layer of these networks possesses unique characteristics, further complicating analysis. To authors' knowledge, a comprehensive framework capable of simulating various spreading processes across different layers, particularly in networks with millions of nodes and connections, has been notably absent. This study introduces a novel framework that efficiently predicts Markov Chain processes over large-scale networks, while significantly reducing time and space complexity. This approach enables exact simulation of spreading processes across extensive real-world multi-layer networks, accounting for diverse influencers on each layer. FastGEMF provides a baseline framework for exact simulating stochastic spread processes, facilitating comparative analysis of models across diverse domains, from epidemiology to social media dynamics.

cs.SI↗

arXiv2023

Multi-Priority Graph Sparsification

A \emph{sparsification} of a given graph $G$ is a sparser graph (typically a subgraph) which aims to approximate or preserve some property of $G$. Examples of sparsifications include but are not limited to spanning trees, Steiner trees, spanners, emulators, and distance preservers. Each vertex has the same priority in all of these problems. However, real-world graphs typically assign different ``priorities'' or ``levels'' to different vertices, in which higher-priority vertices require higher-quality connectivity between them. Multi-priority variants of the Steiner tree problem have been studied in prior literature but this generalization is much less studied for other sparsification problems. In this paper, we define a generalized multi-priority problem and present a rounding-up approach that can be used for a variety of graph sparsifications. Our analysis provides a systematic way to compute approximate solutions to multi-priority variants of a wide range of graph sparsification problems given access to a single-priority subroutine.

cs.DS↗

arXiv2022

Epidemics from the Eye of the Pathogen

While a common trend in disease modeling is to develop models of increasing complexity, it was recently pointed out that outbreaks appear remarkably simple when viewed in the incidence vs. cumulative cases (ICC) plane. This article details the theory behind this phenomenon by analyzing the stochastic SIR (Susceptible, Infected, Recovered) model in the cumulative cases domain. We prove that the Markov chain associated with this model reduces, in the ICC plane, to a pure birth chain for the cumulative number of cases, whose limit leads to an independent increments Gaussian process that fluctuates about a deterministic ICC curve. We calculate the associated variance and quantify the additional variability due to estimating incidence over a finite period of time. We also illustrate the universality brought forth by the ICC concept on real-world data for Influenza A and for the COVID-19 outbreak in Arizona.

q-bio.PE↗

arXiv2021

Approximation algorithms for priority Steiner tree problems

In the Priority Steiner Tree (PST) problem, we are given an undirected graph $G=(V,E)$ with a source $s \in V$ and terminals $T \subseteq V \setminus \{s\}$, where each terminal $v \in T$ requires a nonnegative priority $P(v)$. The goal is to compute a minimum weight Steiner tree containing edges of varying rates such that the path from $s$ to each terminal $v$ consists of edges of rate greater than or equal to $P(v)$. The PST problem with $k$ priorities admits a $\min\{2 \ln |T| + 2, kρ\}$-approximation [Charikar et al., 2004], and is hard to approximate with ratio $c \log \log n$ for some constant $c$ [Chuzhoy et al., 2008]. In this paper, we first strengthen the analysis provided by [Charikar et al., 2004] for the $(2 \ln |T| + 2)$-approximation to show an approximation ratio of $\lceil \log_2 |T| \rceil + 1 \le 1.443 \ln |T| + 2$, then provide a very simple, parallelizable algorithm which achieves the same approximation ratio. We then consider a more difficult node-weighted version of the PST problem, and provide a $(2 \ln |T|+2)$-approximation using extensions of the spider decomposition by [Klein \& Ravi, 1995]. This is the first result for the PST problem in node-weighted graphs. Moreover, the approximation ratios for all above algorithms are tight.

cs.DS↗

arXiv2021

Computing Steiner Trees using Graph Neural Networks

Graph neural networks have been successful in many learning problems and real-world applications. A recent line of research explores the power of graph neural networks to solve combinatorial and graph algorithmic problems such as subgraph isomorphism, detecting cliques, and the traveling salesman problem. However, many NP-complete problems are as of yet unexplored using this method. In this paper, we tackle the Steiner Tree Problem. We employ four learning frameworks to compute low cost Steiner trees: feed-forward neural networks, graph neural networks, graph convolutional networks, and a graph attention model. We use these frameworks in two fundamentally different ways: 1) to train the models to learn the actual Steiner tree nodes, 2) to train the model to learn good Steiner point candidates to be connected to the constructed tree using a shortest path in a greedy fashion. We illustrate the robustness of our heuristics on several random graph generation models as well as the SteinLib data library. Our finding suggests that the out-of-the-box application of GNN methods does worse than the classic 2-approximation method. However, when combined with a greedy shortest path construction, it even does slightly better than the 2-approximation algorithm. This result sheds light on the fundamental capabilities and limitations of graph learning techniques on classical NP-complete problems.

cs.LG↗

arXiv2021

Weighted Additive Spanners

A \emph{spanner} of a graph $G$ is a subgraph $H$ that approximately preserves shortest path distances in $G$. Spanners are commonly applied to compress computation on metric spaces corresponding to weighted input graphs. Classic spanner constructions can seamlessly handle edge weights, so long as error is measured \emph{multiplicatively}. In this work, we investigate whether one can similarly extend constructions of spanners with purely \emph{additive} error to weighted graphs. These extensions are not immediate, due to a key lemma about the size of shortest path neighborhoods that fails for weighted graphs. Despite this, we recover a suitable amortized version, which lets us prove direct extensions of classic $+2$ and $+4$ unweighted spanners (both all-pairs and pairwise) to $+2W$ and $+4W$ weighted spanners, where $W$ is the maximum edge weight. Specifically, we show that a weighted graph $G$ contains all-pairs (pairwise) $+2W$ and $+4W$ weighted spanners of size $O(n^{3/2})$ and $\widetilde{O}(n^{7/5})$ ($O(np^{1/3})$ and $O(np^{2/7})$) respectively. For a technical reason, the $+6$ unweighted spanner becomes a $+8W$ weighted spanner; closing this error gap is an interesting remaining open problem. That is, we show that $G$ contains all-pairs (pairwise) $+8W$ weighted spanners of size $O(n^{4/3})$ ($O(np^{1/4})$).

cs.DM↗

arXiv2021

Multi-level Weighted Additive Spanners

Given a graph $G = (V,E)$, a subgraph $H$ is an \emph{additive $+β$ spanner} if $\dist_H(u,v) \le \dist_G(u,v) + β$ for all $u, v \in V$. A \emph{pairwise spanner} is a spanner for which the above inequality only must hold for specific pairs $P \subseteq V \times V$ given on input, and when the pairs have the structure $P = S \times S$ for some subset $S \subseteq V$, it is specifically called a \emph{subsetwise spanner}. Spanners in unweighted graphs have been studied extensively in the literature, but have only recently been generalized to weighted graphs. In this paper, we consider a multi-level version of the subsetwise spanner in weighted graphs, where the vertices in $S$ possess varying level, priority, or quality of service (QoS) requirements, and the goal is to compute a nested sequence of spanners with the minimum number of total edges. We first generalize the $+2$ subsetwise spanner of [Pettie 2008, Cygan et al., 2013] to the weighted setting. We experimentally measure the performance of this and several other algorithms for weighted additive spanners, both in terms of runtime and sparsity of output spanner, when applied at each level of the multi-level problem. Spanner sparsity is compared to the sparsest possible spanner satisfying the given error budget, obtained using an integer programming formulation of the problem. We run our experiments with respect to input graphs generated by several different random graph generators: Erdős--Rényi, Watts--Strogatz, Barabási--Albert, and random geometric models. By analyzing our experimental results we developed a new technique of changing an initialization parameter value that provides better performance in practice.

cs.DM↗

arXiv2020

Kruskal-based approximation algorithm for the multi-level Steiner tree problem

We study the multi-level Steiner tree problem: a generalization of the Steiner tree problem in graphs where terminals $T$ require varying priority, level, or quality of service. In this problem, we seek to find a minimum cost tree containing edges of varying rates such that any two terminals $u$, $v$ with priorities $P(u)$, $P(v)$ are connected using edges of rate $\min\{P(u),P(v)\}$ or better. The case where edge costs are proportional to their rate is approximable to within a constant factor of the optimal solution. For the more general case of non-proportional costs, this problem is hard to approximate with ratio $c \log \log n$, where $n$ is the number of vertices in the graph. A simple greedy algorithm by Charikar et al., however, provides a $\min\{2(\ln |T|+1), \ell ρ\}$-approximation in this setting, where $ρ$ is an approximation ratio for a heuristic solver for the Steiner tree problem and $\ell$ is the number of priorities or levels (Byrka et al. give a Steiner tree algorithm with $ρ\approx 1.39$, for example). In this paper, we describe a natural generalization to the multi-level case of the classical (single-level) Steiner tree approximation algorithm based on Kruskal's minimum spanning tree algorithm. We prove that this algorithm achieves an approximation ratio at least as good as Charikar et al., and experimentally performs better with respect to the optimum solution. We develop an integer linear programming formulation to compute an exact solution for the multi-level Steiner tree problem with non-proportional edge costs and use it to evaluate the performance of our algorithm on both random graphs and multi-level instances derived from SteinLib.

cs.DS↗

arXiv2020

Graph Spanners: A Tutorial Review

This tutorial review provides a guiding reference to researchers who want to have an overview of the large body of literature about graph spanners. It reviews the current literature covering various research streams about graph spanners, such as different formulations, sparsity and lightness results, computational complexity, dynamic algorithms, and applications. As an additional contribution, we offer a list of open problems on graph spanners.

cs.DM↗

arXiv2019

Multi-Level Graph Sketches via Single-Level Solvers

Given an undirected weighted graph $G(V,E)$, a constrained sketch over a terminal set $T\subset V$ is a subgraph $G'$ that connects the terminal vertices while satisfying a given set of constraints. Examples include Steiner trees (preserving connectivity among $T$) and subsetwise spanners (preserving shortest path distances up to a stretch factor). Multi-level constrained terminal sketches are generalizations in which terminal vertices require different levels or grades of service and each terminal pair is connected with edges of at least the minimum required level of the two terminals. This paper gives a flexible procedure for computing a broad class of multi-level graph sketches, which encompasses multi-level graph spanners, Steiner trees, and $k$--connected subgraphs as a few special cases. The proposed procedure is modular, i.e., it relies on availability of a single-level solver module (be it an oracle or approximation algorithm). One key result is that an $\ell$--level constrained terminal sketch can be computed with $\log\ell$ queries of the solver module while producing feasible solutions with approximation guarantees independent of $\ell$. Additionally, a new polynomial time algorithm for computing a subsetwise spanner is proposed. We show that for $k\in\N$, $\eps>0$, and $T\subset V$, there is a subsetwise $(2k-1)(1+\eps)$--spanner with total weight $O(|T|^\frac1kW(\ST(G,T)))$, where $W(\ST(G,T))$ is the weight of the Steiner tree of $G$ over the subset $T$. This is the first algorithm and weight guarantee for a multiplicative subsetwise spanner for nonplanar graphs. Numerical experiments are also done to illustrate the performance of the proposed algorithms.

cs.DM↗

arXiv2019

Generalized group-based epidemic model for spreading processes on networks: GgroupEM

We develop a generalized group-based epidemic model (GgroupEM) framework for any compartmental epidemic model (for example; susceptible-infected-susceptible, susceptible-infected-recovered, susceptible-exposed-infected-recovered). Here, a group consists of a collection of individual nodes. This model can be used to understand the important dynamic characteristics of a stochastic epidemic spreading over very large complex networks, being informative about the state of groups. Aggregating nodes by groups, the state space becomes smaller than the individual-based approach at the cost of aggregation error, which is strongly bounded by the isoperimetric inequality. We also develop a mean-field approximation of this framework to further reduce the state-space size. Finally, we extend the GgroupEM to multilayer networks. Since the group-based framework is computationally less expensive and faster than an individual-based framework, then this framework is useful when the simulation time is important.

physics.soc-ph↗

arXiv2019

Approximation algorithms for the vertex-weighted grade-of-service Steiner tree problem

Given a graph $G = (V,E)$ and a subset $T \subseteq V$ of terminals, a \emph{Steiner tree} of $G$ is a tree that spans $T$. In the vertex-weighted Steiner tree (VST) problem, each vertex is assigned a non-negative weight, and the goal is to compute a minimum weight Steiner tree of $G$. We study a natural generalization of the VST problem motivated by multi-level graph construction, the \emph{vertex-weighted grade-of-service Steiner tree problem} (V-GSST), which can be stated as follows: given a graph $G$ and terminals $T$, where each terminal $v \in T$ requires a facility of a minimum grade of service $R(v)\in \{1,2,\ldots\ell\}$, compute a Steiner tree $G'$ by installing facilities on a subset of vertices, such that any two vertices requiring a certain grade of service are connected by a path in $G'$ with the minimum grade of service or better. Facilities of higher grade are more costly than facilities of lower grade. Multi-level variants such as this one can be useful in network design problems where vertices may require facilities of varying priority. While similar problems have been studied in the edge-weighted case, they have not been studied as well in the more general vertex-weighted case. We first describe a simple heuristic for the V-GSST problem whose approximation ratio depends on $\ell$, the number of grades of service. We then generalize the greedy algorithm of [Klein \& Ravi, 1995] to show that the V-GSST problem admits a $(2 \ln |T|)$-approximation, where $T$ is the set of terminals requiring some facility. This result is surprising, as it shows that the (seemingly harder) multi-grade problem can be approximated as well as the VST problem, and that the approximation ratio does not depend on the number of grades of service.

cs.DS↗

arXiv2019

Approximation algorithms and an integer program for multi-level graph spanners

Given a weighted graph $G(V,E)$ and $t \ge 1$, a subgraph $H$ is a \emph{$t$--spanner} of $G$ if the lengths of shortest paths in $G$ are preserved in $H$ up to a multiplicative factor of $t$. The \emph{subsetwise spanner} problem aims to preserve distances in $G$ for only a subset of the vertices. We generalize the minimum-cost subsetwise spanner problem to one where vertices appear on multiple levels, which we call the \emph{multi-level graph spanner} (MLGS) problem, and describe two simple heuristics. Applications of this problem include road/network building and multi-level graph visualization, especially where vertices may require different grades of service. We formulate a 0--1 integer linear program (ILP) of size $O(|E||V|^2)$ for the more general minimum \emph{pairwise spanner problem}, which resolves an open question by Sigurd and Zachariasen on whether this problem admits a useful polynomial-size ILP. We extend this ILP formulation to the MLGS problem, and evaluate the heuristic and ILP performance on random graphs of up to 100 vertices and 500 edges.

cs.DM↗

arXiv2018

Multi-Level Steiner Trees

In the classical Steiner tree problem, given an undirected, connected graph $G=(V,E)$ with non-negative edge costs and a set of \emph{terminals} $T\subseteq V$, the objective is to find a minimum-cost tree $E' \subseteq E$ that spans the terminals. The problem is APX-hard; the best known approximation algorithm has a ratio of $ρ= \ln(4)+\varepsilon < 1.39$. In this paper, we study a natural generalization, the \emph{multi-level Steiner tree} (MLST) problem: given a nested sequence of terminals $T_{\ell} \subset \dots \subset T_1 \subseteq V$, compute nested trees $E_{\ell}\subseteq \dots \subseteq E_1\subseteq E$ that span the corresponding terminal sets with minimum total cost. The MLST problem and variants thereof have been studied under various names including Multi-level Network Design, Quality-of-Service Multicast tree, Grade-of-Service Steiner tree, and Multi-Tier tree. Several approximation results are known. We first present two simple $O(\ell)$-approximation heuristics. Based on these, we introduce a rudimentary composite algorithm that generalizes the above heuristics, and determine its approximation ratio by solving a linear program. We then present a method that guarantees the same approximation ratio using at most $2\ell$ Steiner tree computations. We compare these heuristics experimentally on various instances of up to 500 vertices using three different network generation models. We also present various integer linear programming (ILP) formulations for the MLST problem, and compare their running times on these instances. To our knowledge, the composite algorithm achieves the best approximation ratio for up to $\ell=100$ levels, which is sufficient for most applications such as network visualization or designing multi-level infrastructure.

cs.DS↗

arXiv2018

Contact Adaption during Epidemics: A Multilayer Network Formulation Approach

People change their physical contacts as a preventive response to infectious disease propagations. Yet, only a few mathematical models consider the coupled dynamics of the disease propagation and the contact adaptation process. This paper presents a model where each agent has a default contact neighborhood set, and switches to a different contact set once she becomes alert about infection among her default contacts. Since each agent can adopt either of two possible neighborhood sets, the overall contact network switches among 2^N possible configurations. Notably, a two-layer network representation can fully model the underlying adaptive, state-dependent contact network. Contact adaptation influences the size of the disease prevalence and the epidemic threshold---a characteristic measure of a contact network robustness against epidemics---in a nonlinear fashion. Particularly, the epidemic threshold for the presented adaptive contact network belongs to the solution of a nonlinear Perron-Frobenius (NPF) problem, which does not depend on the contact adaptation rate monotonically. Furthermore, the network adaptation model predicts a counter-intuitive scenario where adaptively changing contacts may adversely lead to lower network robustness against epidemic spreading if the contact adaptation is not fast enough. An original result for a class of NPF problems facilitate the analytical developments in this paper.

cs.SI↗

arXiv2017

Modulus of families of walks on graphs

We introduce the notion of modulus of families of walks on graphs. We show how Beurling's famous criterion for extremality, that was formulated in the continuous case, can be interpreted on graphs as an instance of the Karush-Kuhn-Tucker conditions. We then develop an algorithm to numerically compute modulus using Beurling's criterion as our guide.

math.CO↗

arXiv2016

Transient Analysis of a Resource-limited Recovery Policy for Epidemics: a Retrial Queueing Approach

Knowledge on the dynamics of standard epidemic models and their variants over complex networks has been well-established primarily in the stationary regime, with relatively little light shed on their transient behavior. In this paper, we analyze the transient characteristics of the classical susceptible-infected (SI) process with a recovery policy modeled as a state-dependent retrial queueing system in which arriving infected nodes, upon finding all the limited number of recovery units busy, join a virtual buffer and try persistently for service in order to regain susceptibility. In particular, we formulate the stochastic SI epidemic model with added retrial phenomenon as a finite continuous-time Markov chain (CTMC) and derive the Laplace transforms of the underlying transient state probability distributions and corresponding moments for a closed population of size $N$ driven by homogeneous and heterogeneous contacts. Our numerical results reveal the strong influence of infection heterogeneity and retrial frequency on the transient behavior of the model for various performance measures.

eess.SY↗