Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Atomic Decomposition by Basis Pursuit
SIAM Review
Measuring ISP topologies with rocketfuel
IEEE/ACM Transactions on Networking (TON)
An algebraic approach to practical and scalable overlay network monitoring
Proceedings of the 2004 conference on Applications, technologies, architectures, and protocols for computer communications
NetQuest: a flexible framework for large-scale network measurement
IEEE/ACM Transactions on Networking (TON)
Netscope: practical network loss tomography
INFOCOM'10 Proceedings of the 29th conference on Information communications
Sparse recovery using sparse random matrices
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Network Tomography of Binary Network Performance Characteristics
IEEE Transactions on Information Theory
The use of end-to-end multicast measurements for characterizing internal network behavior
IEEE Communications Magazine
IEEE Journal on Selected Areas in Communications
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We study network loss tomography based on observing average loss rates over a set of paths forming a tree --- a severely underdetermined linear problem for the unknown link loss probabilities. We examine in detail the role of sparsity as a regularising principle, pointing out that the problem is technically distinct from others in the compressed sensing literature. While sparsity has been applied in the context of tomography, key questions regarding uniqueness and recovery remain unanswered. Our work exploits the tree structure of path measurements to derive sufficient conditions for sparse solutions to be unique and the condition that ℓ1 minimization recovers the true underlying solution. We present a fast single-pass linear algorithm for ℓ1 minimization and prove that a minimum ℓ1 solution is both unique and sparsest for tree topologies. By considering the placement of lossy links within trees, we show that sparse solutions remain unique more often than is commonly supposed. We prove similar results for a noisy version of the problem.