Memory Efficient Anonymous Graph Exploration

Abstract

Abstract. Efficient exploration of unknown or unmapped environments has become one of the fundamental problem domains in algorithm design. Its applications range from robot navigation in hazardous environments to rigorous searching, indexing and analysing digital data available on the Internet. A large number of exploration algorithms has been proposed under various assumptions about the capability of mobile (exploring) entities and various characteristics of the environment which are to be explored. This paper considers the graph model, where the environment is represented by a graph of connections in which discrete moves are permitted only along its edges. Designing efficient exploration algorithms in this model has been extensively studied under a diverse set of assumptions, e.g., directed vs undirected graphs, anonymous nodes vs nodes with distinct identities, deterministic vs probabilistic solutions, single vs multiple agent exploration, as well as in the context of different complexity measures including the time complexity, the memory consumption, and the use of other computational resources such as tokens and messages. In this work the emphasis is on memory efficient exploration of anonymous graphs. We discuss in more detail three approaches: random walk, Propp machine and basic walk, reviewing major relevant results, presenting recent developments, and commenting on directions for further research.

Random Walks, Interacting Particles, Dynamic Networks: Randomness Can Be Helpful

“…In [30] the authors consider a deterministic walk, the basic walk. The idea of the walk is based on an observation that one can cover the symmetric digraph counterpart of a graph by a collection of directed cycles.…”

Limit Behavior of the Multi-agent Rotor-Router System

“…At discrete, synchronous steps, the tokens are propagated according to the deterministic round robin rule, where after sending each token, the pointer is advanced to the next exit port in the fixed cyclic ordering. Such a mechanism has been proposed as a viable alternative to stochastic and random-walk-based processes in the context of load balancing problems [5,7,9], exploration of graphs [1,8,10,12,15], and stabilization of distributed processes [3,6,17,22].…”

Verification of Asynchronous Mobile-Robots in Partially-Known Environments

“…However, in that paper, the decidability result (and the corresponding logic RTL) was only for one-robot systems (i.e., k = 1), and the undecidability result for k = 2 was for multiple robots that move synchronously and have remote tests. The distributed-computing community has proposed and studied a number of models of robot systems, e.g., recently [24,18,10,13,8,17]. This literature is mostly mathematical, and theorems from this literature are parameterised, i.e., they may involve graph-parameters (e.g., the maximum degree, the number of vertices, the diameter), memory parameters (e.g., the number of internal states of the robot protocol), and the number of robots may be a parameter.…”