On bootstrapping topology knowledge in anonymous networks

Abstract

In this article, we quantify the amount of "practical" information (i.e., views obtained from the neighbors, colors attributed to the nodes and links) to obtain "theoretical" information (i.e., the local topology of the network up to distance k) in anonymous networks. In more detail, we show that a coloring at distance 2k + 1 is necessary and sufficient to obtain the local topology at distance k that includes outgoing links. This bound drops to 2k when outgoing links are not needed. A second contribution of this article deals with color bootstrapping (from which local topology can be obtained using the aforementioned mechanisms). On the negative side, we show that (i) with a distributed daemon, it is impossible to achieve deterministic color bootstrap, even if the whole network topology can be instantaneously obtained, and (ii) with a central daemon, it is impossible to achieve distance m when instantaneous topology knowledge is limited to m − 1. On the positive side, we show that (i) under the k-central daemon, deterministic self-stabilizing bootstrap of colors up to distance k is possible provided that k-local topology can be instantaneously obtained, and (ii) under the distributed daemon, probabilistic self-stabilizing bootstrap is possible for any range.

Ressource Efficient Stabilization for Local Tasks despite Unknown Capacity Links

“…, ∆ `1u in networks with nodes with maximum degree ∆. Vertex coloring is one of the most studied tasks in distributed network computing in general, and in self-stabilization in particular, as witnessed by numerous contributions: [2,3,4,5,15,17,18,20,21,22]. While most previous work about self-stabilizing vertex coloring considered the state model (see [4,5,15,17,22]), a few paper considered the message passing model [2,18,20,21].…”

“…Vertex coloring is one of the most studied tasks in distributed network computing in general, and in self-stabilization in particular, as witnessed by numerous contributions: [2,3,4,5,15,17,18,20,21,22]. While most previous work about self-stabilizing vertex coloring considered the state model (see [4,5,15,17,22]), a few paper considered the message passing model [2,18,20,21]. However, all existing solutions for this latter model provide probabilistic guarantees only [2,18,20,21], and most of them assume some strong or weak forms of synchronous execution model [2,18,21].…”

“…While most previous work about self-stabilizing vertex coloring considered the state model (see [4,5,15,17,22]), a few paper considered the message passing model [2,18,20,21]. However, all existing solutions for this latter model provide probabilistic guarantees only [2,18,20,21], and most of them assume some strong or weak forms of synchronous execution model [2,18,21]. To our knowledge, there are no deterministic self-stabilizing vertex coloring protocols that operate in the asynchronous message passing setting, where the number of initial spurious messages in communication links is unknown to the participating processes.…”

Self-Stabilizing Algorithms

“…Other variations are also possible (for example, a k-locally central scheduling [62]: at a given moment, in each neighborhood of node at distance at most k, only one of the nodes executes it code), but in practice, they are equivalent to one of the three models above (see [69,71]). The more constrained the spatial scheduling model is, the easier it is to solve problems.…”

Self-stabilizing TDMA algorithms for wireless ad-hoc networks without external reference

“…The proposal in [9] considers shared variable emulation. Several selfstabilizing algorithms adopt this abstraction, e.g., a generalized version of the dining philosophers problem for wireless networks in [6], topology discovery in anonymous networks [19], random distance-k vertex coloring [20], deterministic distance-2 vertex coloring [3], two-hop conflict resolution [25], a transformation from central demon models to distributed scheduler ones [27], to name a few. The aforementioned algorithms assume that if a node transmits infinitely many messages, all of its communication neighbors will receive infinitely many of them.…”