Fast Approximation Algorithms for Near-optimal Large-scale Network Monitoring

Michael Kallitsis; Stilian Stoev; George Michailidis

Home/Archive/arXiv

arXiv · 1108.3048

Fast Approximation Algorithms for Near-optimal Large-scale Network Monitoring

Michael Kallitsis·Stilian Stoev·George Michailidis

View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the problem of optimal traffic prediction and monitoring in large-scale networks. Our goal is to determine which subset of K links to monitor in order to "best" predict the traffic on the remaining links in the network. We consider several optimality criteria. This can be formulated as a combinatorial optimization problem, belonging to the family of subset selection problems. Similar NP-hard problems arise in statistics, machine learning and signal processing. Some include subset selection for regression, variable selection, and sparse approximation. Exact solutions are computationally prohibitive. We present both new heuristics as well as new efficient algorithms implementing the classical greedy heuristic - commonly used to tackle such combinatorial problems. Our approach exploits connections to principal component analysis (PCA), and yields new types of performance lower bounds which do not require submodularity of the objective functions. We show that an ensemble method applied to our new randomized heuristic algorithm, often outperforms the classical greedy heuristic in practice. We evaluate our algorithms under several large-scale networks, including real life networks.

Explore related subjects

cs.DS

Keep this discovery

BibTeX RIS

Michael Kallitsis, Stilian Stoev, George Michailidis. 2011-08-15. Fast Approximation Algorithms for Near-optimal Large-scale Network Monitoring. https://arxiv.org/abs/1108.3048

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↗