Distributed CONGEST Algorithms against Mobile Adversaries

Orr Fischer; Merav Parter

Home/Archive/arXiv

arXiv · 2305.14300

Distributed CONGEST Algorithms against Mobile Adversaries

Orr Fischer·Merav Parter

View original source ↗Read source document ↗Export metadata ↓

Abstract

In their seminal PODC 1991 paper, Ostrovsky and Yung introduced the study of distributed computation in the presence of mobile adversaries which can dynamically appear throughout the network. Over the years, this setting has been studied mostly under the assumption that the communication graph is fully-connected. Resilient CONGEST algorithms for general graphs, on the other hand, are currently known only for the classical static setting, i.e., where the set of corrupted edges (or nodes) is fixed throughout the entire computation. We fill this gap by providing round-efficient simulations that translate given CONGEST algorithms into equivalent algorithms that are resilient against $f$-mobile edge adversaries. Our main results are: -Perfect-Security with Mobile Eavesdroppers: A translation of any $r$-round $f$-static-secure algorithm into an equivalent $\Theta(f)$-mobile-secure algorithm with $\Theta(r)$ rounds. We also show that the $f$-static-secure algorithms of [Hitron, Parter and Yogev, DISC 2022 & ITCS 2023] can be modified into $f$-mobile-secure algorithms with the same number of rounds. -Resilience with Mobile Byzantine Adversaries: An $f$-mobile-byzantine simulation which is based on a decomposition of the graph into low-diameter edge-disjoint spanning trees. This provides us with near-optimal CONGEST compilers for expander graphs. It also leads to near-optimal compilers in the congested-clique model against $\Theta(n)$-mobile adversaries. For general $(2f+1)$ edge-connected graphs with $f$-mobile adversary, we almost match the bounds known for the $f$-static setting, when provided a trusted pre-processing phase. Our results are based on a collection of tools from interactive coding [Gelles, Found. Trends Theor. Comput. Sci. 2017], linear sketches and low-congestion graph decomposition. The introduced toolkit might have further applications for resilient computation.

Explore related subjects

cs.DS cs.DC

Keep this discovery

BibTeX RIS

Orr Fischer, Merav Parter. 2023-05-23. Distributed CONGEST Algorithms against Mobile Adversaries. https://arxiv.org/abs/2305.14300

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗

arXiv2026

A deterministic $(1+\varepsilon)^n$ approximation for the permanent of a nonnegative matrix

For every fixed $0<\varepsilon\le1$, we give a deterministic strongly polynomial algorithm that, given a nonnegative matrix $A\in\mathbb{R}_{\ge0}^{n\times n}$, returns $Q$ satisfying $\operatorname{per} A\le Q\le(1+\varepsilon)^n\operatorname{per} A$.

cs.DS↗

arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗