David Pokrass Jacobs

Self-stabilizing Algorithms for Minimal Dominating Sets and Maximal Independent Sets

In the self-stabilizing algorithmic paradigm for distributed computation each node has only a local view of the system, yet in a finite amount of time, the system converges to a global state satisfying some desired property. In this paper we present polynomial time self-stabilizing algorithms for finding a dominating bipartition, a maximal independent set, and a minimal dominating set in any graph.

Self-stabilizing protocols for maximal matching and maximal independent sets for ad hoc networks

We propose two distributed algorithms to maintain, respectively, a maximal matching and a maximal independent set in a given ad hoc network; our algorithms are fault tolerant (reliable) in the sense that the algorithms can detect occasional link failures and/or new link creations in the network (due to mobility of the hosts) and can readjust the global predicates. We provide time complexity analysis of the algorithms in terms of the number of rounds needed for the algorithm to stabilize after a topology change, where a round is defined as a period of time in which each node in the system receives beacon messages from all its neighbors. In any ad hoc network, the participating nodes periodically transmit beacon messages for message transmission as well as to maintain the knowledge of the local topology at the node; as a result, the nodes get the information about their neighbor nodes synchronously (at specific time intervals). Thus, the paradigm to analyze the complexity of the self-stabilizing algorithms in the context of ad hoc networks is very different from the traditional concept of an adversary daemon used in proving the convergence and correctness of self-stabilizing distributed algorithms in general.

Maximal matching stabilizes in time O( m )

Abstract On a network having m edges and n nodes, Hsu and Huangs self-stabilizing algorithm for maximal matching stabilizes in at most 2m+n moves.

A simple heuristic for maximizing service of carousel storage

Abstract We consider a system that stores cases of items. Items are removed from storage in groups. A group consists of a certain number of items of each type. The (integer maximization) problem is to determine how many cases of each type should be stored in order to maximize the number of groups of items that can be retrieved without re-loading. We give a simple heuristic that yields a feasible solution whose error can be bounded. Our method takes only linear time. Scope and purpose Performance of an automated storage and retrieval system such as a carousel depends greatly upon the way it is loaded. Commonly a carousel will be loaded with cases of items that will be retrieved in groups. A group is a certain number of items of each type. For example, a group might constitute the parts needed to manufacture one instance of a product. Typically the carousel operator wants to retrieve as many groups as possible without running out of items of any type. We present a simple heuristic that prescribes how many cases of each item type should be loaded. The number of groups supplied by our solution is close to optimal. The solution is given by explicit equations, and can be computed in time linear in the number of item types.

Distance- k knowledge in self-stabilizing algorithms

Many graph problems seem to require knowledge that extends beyond the immediate neighbors of a node. The usual self-stabilizing model only allows for nodes to make decisions based on the states of their immediate neighbors. We provide a general transformation for constructing self-stabilizing algorithms which utilize distance-k knowledge. Our transformation has both a slowdown and space overhead in n^O^(^l^o^g^k^), and might be thought of as a distance-k resource allocation algorithm. Our main application is a polynomial-time self-stabilizing algorithm for finding maximal irredundant sets, a problem which seems to require distance-4 information. These results can be generalized to efficiently find maximal P-sets, for properties P which we call local monotonic. Our techniques extend results in a recent paper by Gairing et al. for achieving distance-two information.

The Private Neighbor Cube

Let

On the computational complexity of upper fractional domination

S

Reducing the adjacency matrix of a tree

be a set of vertices in a graph

Domination Subdivision Numbers

G = (V, E)

Self-Stabilizing Graph Protocols

. The authors state that a vertex u in S has a private neighbor (relative to