Optimal constrained graph exploration

Duncan, Christian A.; Kobourov, Stephen G.; Kumar, V. S. Anil

doi:10.1145/1159892.1159897

Cited by 77 publications

(88 citation statements)

References 24 publications

(26 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, the geometric setting of exploring grid graphs with and without holes is considered by [10,11,14,15,17], where a variety of competitive algorithms with constant competitive ratios is provided. A related setting is studied in [4], where an agent has to explore a graph while being attached to the starting point by a rope of restricted length. A similar setting is considered in [1], in which each agent has to return regularly to the starting point, for example for refueling.…”

Section: Related Workmentioning

confidence: 99%

Fast collaborative graph exploration

Dereniowski

Disser

Kosowski

et al. 2015

Information and Computation

View full text Add to dashboard Cite

We study the following scenario of online graph exploration. A team of k agents is initially located at a distinguished vertex r of an undirected graph. At every time step, each agent can traverse an edge of the graph. All vertices have unique identifiers, and upon entering a vertex, an agent obtains the list of identifiers of all its neighbors. We ask how many time steps are required to complete exploration, i.e., to make sure that every vertex has been visited by some agent.We consider two communication models: one in which all agents have global knowledge of the state of the exploration, and one in which agents may only exchange information when simultaneously located at the same vertex. As our main result, we provide the first strategy which performs exploration of a graph with n vertices at a distance of at most D from r in time O(D), using a team of agents of polynomial size k = Dn 1+ < n 2+ , for any > 0. Our strategy works in the local communication model, without knowledge of global parameters such as n or D.We also obtain almost-tight bounds on the asymptotic relation between exploration time and team size, for large k.

show abstract

Section: Related Workmentioning

confidence: 99%

Fast collaborative graph exploration

Dereniowski

Disser

Kosowski

et al. 2015

Information and Computation

View full text Add to dashboard Cite

show abstract

“…In some papers, additional restrictions on the moves of the robot are imposed. It is assumed that the robot has either a restricted tank [5,8], forcing it to periodically return to the base for refueling, or that it is tethered, i.e., attached to the base by a rope or cable of restricted length [17].…”

Section: Related Workmentioning

confidence: 99%

Computing Without Communicating: Ring Exploration by Asynchronous Oblivious Robots

et al. 2012

View full text Add to dashboard Cite

Abstract. We consider the problem of exploring an anonymous unoriented ring by a team of k identical, oblivious, asynchronous mobile robots that can view the environment but cannot communicate. This weak scenario is standard when the spatial universe in which the robots operate is the two-dimentional plane, but (with one exception) has not been investigated before. We indeed show that, although the lack of these capabilities renders the problems considerably more difficult, ring exploration is still possible. We show that the minimum number ρ(n) of robots that can explore a ring of size n is O(log n) and that ρ(n) = Ω(log n) for arbitrarily large n. On one hand we give an algorithm that explores the ring starting from any initial configuration, provided that n and k are co-prime, and we show that there always exist such k in O(log n). On the other hand we show that Ω(log n) agents are necessary for arbitrarily large n. Notice that, when k and n are not co-prime, the problem is sometimes unsolvable (i.e., there are initial configurations for which the exploration cannot be done). This is the case, e.g., when k divides n.

show abstract

“…In [12,13,4,14,15,16,17], the explored graph is undirected and the agent can traverse edges in both directions. Also, two alternative e ciency measures are adopted in most papers devoted to graph exploration, namely, the time of completing the task [7,12,8,9,13,10,14], or the number of memory bits (states in the automaton) available to the agent.…”

Section: Related Workmentioning

confidence: 99%

More Efficient Periodic Traversal in Anonymous Undirected Graphs

Czyzowicz

Dobrev

Gąsieniec

et al. 2010

Structural Information and Communication Complexity

View full text Add to dashboard Cite

Abstract. We consider the problem of periodic graph exploration in which a mobile entity with (at most) constant memory, an agent, has to visit all n nodes of an arbitrary undirected graph G in a periodic manner. Graphs are supposed to be anonymous, that is, nodes are unlabeled. However, while visiting a node, the robot has to distinguish between edges incident to it. For each node v the endpoints of the edges incident to v are uniquely identi ed by di erent integer labels called port numbers. We are interested in the minimisation of the length of the exploration period. This problem is unsolvable if the local port numbers are set arbitrarily, see [1]. However, surprisingly small periods can be achieved when assigning carefully the local port numbers. Dobrev et al. [2] described an algorithm for assigning port numbers, and an oblivious agent (i.e., an agent with no persistent memory) using it, such that the agent explores all graphs of size n within period 10n. Providing the agent with a constant number of memory bits, the optimal length of the period was proved in [3] to be no more than 3.75n (using a di erent assignment of the port numbers). In this paper, we improve both these bounds. More precisely, we show a period of length at most 4 1 3 n for oblivious agents, and a period of length at most 3.5n for agents with constant memory. Finally, we give the rst non-trivial lower bound, 2.8n, on the period length for the oblivious case.

show abstract

Optimal constrained graph exploration

Cited by 77 publications

References 24 publications

Fast collaborative graph exploration

Fast collaborative graph exploration

Computing Without Communicating: Ring Exploration by Asynchronous Oblivious Robots

More Efficient Periodic Traversal in Anonymous Undirected Graphs

Contact Info

Product

Resources

About