Fast collaborative graph exploration

Dereniowski, Dariusz; Disser, Yann; Kosowski, Adrian; Pająk, Dominik; Uznański, Przemysław

doi:10.1016/j.ic.2014.12.005

Cited by 52 publications

(23 citation statements)

References 20 publications

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“…One problem closely related to Dispersion is the graph exploration by mobile robots. The exploration problem has been heavily studied in the literature for specific as well as arbitrary graphs, e.g., [2,4,8,13,17]. It was shown that a robot can explore an anonymous graph using Θ(D log ∆)-bits memory; the runtime of the algorithm is O(∆ D+1 ) [13].…”

Section: Algorithm Memory Per Robot Time (In Rounds) (In Bits)mentioning

confidence: 99%

“…Algorithm 1: Algorithm Graph Disperse(k) to solve Dispersion. 1 if i is alone at node then 2 i.settled ← 1; do not set i.treelabel 3 for pass = 1, log k do 4 Stage 1 (Graph DFS: for group dispersion of unsettled robots) 5 for round = 0, min(4m − 2n + 2, k∆) do 6 if visited node is free then 7 highest ID robot r settles; r.treelabel ← x.ID, where x is robot with lowest ID 8 x continues its DFS after r sets its parent, child for DFS of x reset parent, child, treelabel, mult, home // Lexico-priority: (mult, treelabel/ID). Higher mult is higher priority; if mult is equal, lower treelabel/ID has higher priority.…”

Section: Stagementioning

confidence: 99%

See 1 more Smart Citation

Fast Dispersion of Mobile Robots on Arbitrary Graphs

Kshemkalyani

Molla

Sharma

2019

Algorithms for Sensor Systems

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The mobile robot dispersion problem on graphs asks k ≤ n robots placed initially arbitrarily on the nodes of an n-node anonymous graph to reposition autonomously to reach a configuration in which each robot is on a distinct node of the graph. This problem is of significant interest due to its relationship to other fundamental robot coordination problems, such as exploration, scattering, load balancing, and relocation of self-driven electric cars (robots) to recharge stations (nodes). In this paper, we provide two novel deterministic algorithms for dispersion, one for arbitrary graphs and another for grid graphs, in a synchronous setting where all robots perform their actions in every time step. Our algorithm for arbitrary graphs has O(min(m, k∆) · log k) steps runtime using O(log n) bits of memory at each robot, where m is the number of edges and ∆ is the maximum degree of the graph. This is an exponential improvement over the O(mk) steps best previously known algorithm. In particular, the runtime of our algorithm is optimal (up to a O(log k) factor) in constant-degree arbitrary graphs. Our algorithm for grid graphs has O(min(k, √ n)) steps runtime using Θ(log k) bits at each robot. This is the first algorithm for dispersion in grid graphs. Moreover, this algorithm is optimal for both memory and time when k = Ω(n). problem). This problem has many practical applications, for example, in relocating selfdriven electric cars (robots) to recharge stations (nodes), assuming that the cars have smart devices to communicate with each other to find a free/empty charging station [1,16]. This problem is also important due to its relationship to many other well-studied autonomous robot coordination problems, such as exploration, scattering, load balancing, covering, and self-deployment [1,16]. One of the key aspects of mobile-robot research is to understand how to use the resource-limited robots to accomplish some large task in a distributed manner [10,11]. In this paper, we study the trade-off between memory requirement of robots and the time to solve Dispersion on graphs.Augustine and Moses Jr.[1] studied Dispersion assuming k = n. They proved a memory lower bound of Ω(log n) bits at each robot and a time lower bound of Ω(D) (Ω(n) in arbitrary graphs) for any deterministic algorithm in any graph, where D is the diameter of the graph. They then provided deterministic algorithms using O(log n) bits at each robot to solve Dispersion on lines, rings, and trees in O(n) time. For arbitrary graphs, they provided two algorithms, one using O(log n) bits at each robot with O(mn) time and another using O(n log n) bits at each robot with O(m) time, where m is the number of edges in the graph. Recently, Kshemkalyani and Ali [16] provided an Ω(k) time lower bound for arbitrary graphs for k ≤ n. They then provided three deterministic algorithms for Dispersion in arbitrary graphs: (i) The first algorithm using O(k log ∆) bits at each robot with O(m) time, (ii) The second algorithm using O(D log ∆) bits at each robot with O(∆ D ) time, and ...

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Section: Algorithm Memory Per Robot Time (In Rounds) (In Bits)mentioning

confidence: 99%

Section: Stagementioning

confidence: 99%

Fast Dispersion of Mobile Robots on Arbitrary Graphs

Kshemkalyani

Molla

Sharma

2019

Algorithms for Sensor Systems

View full text Add to dashboard Cite

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“…1. what parameters of the graph are known to the robots, 2. whether the graph is anonymous, 3. whether memory is allowed at robots [13], 4. whether memory is allowed at the nodes [7], 5. whether knowledge of the incoming ports through which a robot enters nodes is allowed [13], 6. whether exploration is by a single robot or cooperating robots [5], [6], [9], 7. if exploration is by multiple robots, whether robots are allowed to communicate under the local communication model or the global communication model [5], [6], [9], 8. if exploration is by multiple robots, whether robots are colocated or dispersed in the initial configuration, 9. whether we are designing a solution that is time optimal, or space optimal, 10. whether the bounds on memory are subject to time optimality solutions, 11. whether termination of the robot is required (and if so, whether at the starting node) or it is to perpetually traverse the graph…”

Section: Related Workmentioning

confidence: 99%

“…Thereafter, each traversal of the graph takes up to O(∆ 10 m) time steps. Dereniowski et al [9] studied the trade-off between graph exploration time and number of robots, assuming that (i) nodes have unique identifiers, (ii) when visiting a node, a list of all its neighbors is also known, (iii) all the robots are located at one node in the initial configuration, (iv) robots have unique identifiers, and (v) there is no bound on the memory of robots, which construct a map of the previously visited subgraph. The authors considered results in both the local communication model, as well as the global communication model.…”

Section: Related Workmentioning

confidence: 99%

Efficient dispersion of mobile robots on graphs

Kshemkalyani

Ali

2019

Proceedings of the 20th International Conference on Distributed Computing and Networking

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The dispersion problem on graphs requires k robots placed arbitrarily at the n nodes of an anonymous graph, where k ≤ n, to coordinate with each other to reach a final configuration in which each robot is at a distinct node of the graph. The dispersion problem is important due to its relationship to graph exploration by mobile robots, scattering on a graph, and load balancing on a graph. In addition, an intrinsic application of dispersion has been shown to be the relocation of self-driven electric cars (robots) to recharge stations (nodes). We propose three efficient algorithms to solve dispersion on graphs. Our algorithms require O(k log ∆) bits at each robot, and O(m) steps running time, where m is the number of edges and ∆ is the degree of the graph. The algorithms differ in whether they address the synchronous or the asynchronous system model, and in what, where, and how data structures are maintained.

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“…However, optimization of the search by the use of multiple robots often involves coordination issues, where the searchers need to communicate in order to synchronize their efforts and adequately split the entire task into portions assigned to individual robots (cf. [13,23,25,27]). As this objective is often not easy to achieve, some multi-robot search problems turn out to be NP-hard (e.g., see [27]).…”

Section: Related Workmentioning

confidence: 99%

Linear Search by a Pair of Distinct-Speed Robots

Bampas¹,

Czyzowicz²,

Gąsieniec³

et al. 2016

Structural Information and Communication Complexity

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Two mobile robots are initially placed at the same point on an infinite line. Each robot may move on the line in either direction not exceeding its maximal speed. The robots need to find a stationary target placed at an unknown location on the line. The search is completed when both robots arrive at the target point. The target is discovered at the moment when either robot arrives at its position. The robot knowing the placement of the target may communicate it to the other robot. We look 123Algorithmica for the algorithm with the shortest possible search time (i.e. the worst-case time at which both robots meet at the target) measured as a function of the target distance from the origin (i.e. the time required to travel directly from the starting point to the target at unit velocity). We consider two standard models of communication between the robots, namely wireless communication and communication by meeting. In the case of communication by meeting, a robot learns about the target while sharing the same location with a robot possessing this knowledge. We propose here an optimal search strategy for two robots including the respective lower bound argument, for the full spectrum of their maximal speeds. This extends the main result of Chrobak et al. (in: Italiano, Margaria-Steffen, Pokorný, Quisquater, Wattenhofer (eds) Current trends in theory and practice of computer science, SOFSEM, 2015) referring to the exact complexity of the problem for the case when the speed of the slower robot is at least one third of the faster one. In the wireless communication model, a message sent by one robot is instantly received by the other robot, regardless of their current positions on the line. For this model, we design a strategy which is optimal whenever the faster robot is at most √ 17 + 4 ≈ 8.123 times faster than the slower one. We also prove that otherwise the wireless communication offers no advantage over communication by meeting.

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Fast collaborative graph exploration

Cited by 52 publications

References 20 publications

Fast Dispersion of Mobile Robots on Arbitrary Graphs

Fast Dispersion of Mobile Robots on Arbitrary Graphs

Efficient dispersion of mobile robots on graphs

Linear Search by a Pair of Distinct-Speed Robots

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