11,760 research outputs found
Space-Time Tradeoffs for Distributed Verification
Verifying that a network configuration satisfies a given boolean predicate is
a fundamental problem in distributed computing. Many variations of this problem
have been studied, for example, in the context of proof labeling schemes (PLS),
locally checkable proofs (LCP), and non-deterministic local decision (NLD). In
all of these contexts, verification time is assumed to be constant. Korman,
Kutten and Masuzawa [PODC 2011] presented a proof-labeling scheme for MST, with
poly-logarithmic verification time, and logarithmic memory at each vertex.
In this paper we introduce the notion of a -PLS, which allows the
verification procedure to run for super-constant time. Our work analyzes the
tradeoffs of -PLS between time, label size, message length, and computation
space. We construct a universal -PLS and prove that it uses the same amount
of total communication as a known one-round universal PLS, and factor
smaller labels. In addition, we provide a general technique to prove lower
bounds for space-time tradeoffs of -PLS. We use this technique to show an
optimal tradeoff for testing that a network is acyclic (cycle free). Our
optimal -PLS for acyclicity uses label size and computation space . We further describe a recursive space verifier for
acyclicity which does not assume previous knowledge of the run-time .Comment: Pre-proceedings version of paper presented at the 24th International
Colloquium on Structural Information and Communication Complexity (SIROCCO
2017
Space-Time Sampling for Network Observability
Designing sparse sampling strategies is one of the important components in
having resilient estimation and control in networked systems as they make
network design problems more cost-effective due to their reduced sampling
requirements and less fragile to where and when samples are collected. It is
shown that under what conditions taking coarse samples from a network will
contain the same amount of information as a more finer set of samples. Our goal
is to estimate initial condition of linear time-invariant networks using a set
of noisy measurements. The observability condition is reformulated as the frame
condition, where one can easily trace location and time stamps of each sample.
We compare estimation quality of various sampling strategies using estimation
measures, which depend on spectrum of the corresponding frame operators. Using
properties of the minimal polynomial of the state matrix, deterministic and
randomized methods are suggested to construct observability frames. Intrinsic
tradeoffs assert that collecting samples from fewer subsystems dictates taking
more samples (in average) per subsystem. Three scalable algorithms are
developed to generate sparse space-time sampling strategies with explicit error
bounds.Comment: Submitted to IEEE TAC (Revised Version
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