The Robot Crawler Number of a Graph

Bonato, Anthony; Rio-Chanona, R. Maria del; MacRury, Calum; Nicolaidis, Jake; Pérez‐Giménez, Xavier; Prałat, Paweł; Ternovsky, Kirill

doi:10.1007/978-3-319-26784-5_11

Cited by 4 publications

(7 citation statements)

References 32 publications

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“…where the case q ≤ j follows immediately from (12) (since 2/j ≤ 1 q 2 √ q/j), and the case q ≥ j is trivially true (since the right-hand side of (13) is greater than 1). Combining (11) and (13) together and using the fact that H holds a.a.s., we conclude that…”

Section: Relationship Between G N M and G N M−oldmentioning

confidence: 99%

“…In [11], a simplified model for crawling complex networks such as the web graph was proposed, which is a variation of the robot vacuum edge-cleaning process introduced earlier by Messinger and Nowakowski [28]. In particular, it was shown that a.a.s.…”

Section: Lower Boundmentioning

confidence: 99%

“…In particular, it was shown that a.a.s. the preferential attachment model G n 2 has the following property: the optimal robot crawler needs substantially more than n steps to visit all the vertices of the graph (see Theorem 10 in [11] and the discussion preceding it). This immediately implies (in a strong sense) that G n 2 is not Hamiltonian a.a.s.…”

Section: Lower Boundmentioning

confidence: 99%

“…Here we briefly recall the main ingredients of the argument in [11] without reference to the robot crawling process. Fix some constant c ∈ (0, 1) and consider G n 2 .…”

Section: Lower Boundmentioning

confidence: 99%

“…Moreover, these observations, combined with an additional argument presented below, show a stronger property, namely, that G n 2 has no perfect matching a.a.s. Here we briefly recall the the main ingredients of the argument in [11] without reference to the robot crawling process. Fix some constant c ∈ (0, 1) and consider G n 2 .…”

Section: Lower Boundmentioning

confidence: 99%

See 4 more Smart Citations

Perfect matchings and Hamiltonian cycles in the preferential attachment model

Frieze

Pérez‐Giménez

Prałat

et al. 2018

Random Struct Algorithms

Self Cite

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In this paper, we study the existence of perfect matchings and Hamiltonian cycles in the preferential attachment model.In this model, vertices are added to the graph one by one, and each time a new vertex is created it establishes a connection with m random vertices selected with probabilities proportional to their current degrees. (Constant m is the only parameter of the model.) We prove that if m ≥ 1253, then asymptotically almost surely there exists a perfect matching.

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Section: Relationship Between G N M and G N M−oldmentioning

confidence: 99%

Section: Lower Boundmentioning

confidence: 99%

Section: Lower Boundmentioning

confidence: 99%

“…Here we briefly recall the main ingredients of the argument in [11] without reference to the robot crawling process. Fix some constant c ∈ (0, 1) and consider G n 2 .…”

Section: Lower Boundmentioning

confidence: 99%

Section: Lower Boundmentioning

confidence: 99%

See 3 more Smart Citations

Perfect matchings and Hamiltonian cycles in the preferential attachment model

Frieze

Pérez‐Giménez

Prałat

et al. 2018

Random Struct Algorithms

Self Cite

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The Robot Crawler Model on Complete k-Partite and Erdős-Rényi Random Graphs

Davidson

Ganesh

2019

Lecture Notes in Computer Science

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Web crawlers are used by internet search engines to gather information about the web graph. In this paper we investigate a simple process which models such software by walking around the vertices of a graph. Once initial random vertex weights have been assigned, the robot crawler traverses the graph deterministically following a greedy algorithm, always visiting the neighbour of least weight and then updating this weight to be the highest overall. We consider the maximum, minimum and average number of steps taken by the crawler to visit every vertex of firstly, complete k-partite graphs and secondly, sparse Erdős-Rényi random graphs. Our work follows on from a paper of Bonato et. al. who introduced the model. *

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Lower Bounds for Graph Exploration Using Local Policies

Akash

Fekete

Lee

et al. 2016

WALCOM: Algorithms and Computation

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We give lower bounds for various natural node-and edgebased local strategies for exploring a graph. We consider this problem both in the setting of an arbitrary graph as well as the abstraction of a geometric exploration of a space by a robot, both of which have been extensively studied. We consider local exploration policies that use time-oflast-visit or alternatively least-frequently-visited local greedy strategies to select the next step in the exploration path. Both of these strategies were previously considered by Cooper et al. (2011) for a scenario in which counters for the last visit or visit frequency are attached to the edges. In this work we consider the case in which the counters are associated with the nodes, which for the case of dual graphs of geometric spaces could be argued to be intuitively more natural and likely more efficient. Surprisingly, these alternate strategies give worst-case superpolynomial/exponential time for exploration, whereas the least-frequentlyvisited strategy for edges has a polynomially bounded exploration time, as shown by Cooper et al. (2011).

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The Robot Crawler Number of a Graph

Cited by 4 publications

References 32 publications

Perfect matchings and Hamiltonian cycles in the preferential attachment model

Perfect matchings and Hamiltonian cycles in the preferential attachment model

The Robot Crawler Model on Complete k-Partite and Erdős-Rényi Random Graphs

Lower Bounds for Graph Exploration Using Local Policies

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