Detecting Locally Distributed Predicates

Abstract

In this paper, we formalize locally distributed predicates, a concept previously introduced to address specific challenges associated with modular robotics and distributed debugging. A locally distributed predicate (LDP) is a novel construction for representing and detecting distributed properties in sparse-topology systems. Previous work on LDPs presented empirical validation; here we show a formal model for two variants of the LDP algorithm, LDP-Basic and LDP-Snapshot, and establish performance bounds for these variants. We prove that LDP-Basic can detect strong stable predicates, that LDP-Snapshot can detect all stable predicates, and discuss their applicability to various distributed programming domains and to spatial computing in general. LDP detection in bounded-degree networks is shown to be scale-free, making the approach particularly attractive for specific topologies even though LDPs are less efficient than snapshot algorithms in general distributed systems.

Detecting Tree Distributed Predicates

“…We then push one step further by studying the problem of detecting stable localityaware predicates, which have stronger detectability compared to strong stable locality-aware predicates. The satisfiability of stable predicates depends on channel states [8], unlike the satisfiability of strong stable predicates which does not depend on channel states.…”

“…We note that, the formalism and algorithm given in [8] can only detect a predicate on a chain or ring topology. This linear topology is not enough for specifying the area of interest.…”

“…We evaluate their complexities using two metrics: message complexity and storage cost. The complexity of the algorithm in [8], which can detect a predicate only on a chain or ring topology, is shown to be related to the degree of the network and the associated topology, rather than the size of the network. Our algorithms share the same scale-free property.…”

“…To make the analysis more meaningful, we compare the complexity of our algorithms with the Chandy-Lamport (CL) snapshot algorithm [3] and the algorithm (LDP-Basic) proposed in [8].…”

“…Inspired by the algorithm in [8], which can detect a stable predicate only on a linear chain or a ring topology, we design a set of algorithms to detect several classes of locality-aware predicates: (i) strong stable conjunctive predicates, (ii) strong stable relational predicates, (iii) stable conjunctive predicates, and (iv) stable relational predicates.…”