Min-Max Latency Walks: Approximation Algorithms for Monitoring Vertex-Weighted Graphs

Alamdari, Soroush; Fata, Elaheh; Smith, Stephen L.

doi:10.1007/978-3-642-36279-8_9

“…A preliminary version of this paper appeared as [1]. Compared to the conference version, this version presents detailed proofs of all statements, new results on the existence of optimal finite walks, additional remarks and illustrative examples, and a new case study on patrolling in the simulations section.…”

Section: Introductionmentioning

confidence: 99%

Persistent monitoring in discrete environments: Minimizing the maximum weighted latency between observations

Alamdari

¹

,

Fata

²

,

Smith

³

2013

The International Journal of Robotics Research

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In this paper, we consider the problem of planning a path for a robot to monitor a known set of features of interest in an environment. We represent the environment as a graph with vertex weights and edge lengths. The vertices represent regions of interest, edge lengths give travel times between regions, and the vertex weights give the importance of each region. As the robot repeatedly performs a closed walk on the graph, we define the weighted latency of a vertex to be the maximum time between visits to that vertex, weighted by the importance (vertex weight) of that vertex. Our goal is to find a closed walk that minimizes the maximum weighted latency of any vertex. We show that there does not exist a polynomial time algorithm for the problem. We then provide two approximation algorithms; an O(log n)-approximation algorithm and an O(log ρ G )-approximation algorithm, where ρ G is the ratio between the maximum and minimum vertex weights. We provide simulation results which demonstrate that our algorithms can be applied to problems consisting of thousands of vertices, and a case study for patrolling a city for crime.

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“…wj , for all i ∈ V , to be a distribution on V , and a randomized trajectory P satisfy π * P = π * . Then, (π * , P) solves (11).…”

Section: B Peak Age Minimizationmentioning

confidence: 99%

“…Proof: If we were to minimize the objective in (11) over the space of all distribution π on V , then the optimal distribution would be…”

Section: B Peak Age Minimizationmentioning

confidence: 99%

See 1 more Smart Citation

Age Optimal Information Gathering and Dissemination on Graphs

Tripathi

¹

,

Talak

²

,

Modiano

³

2023

IEEE Trans. on Mobile Comput.

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We consider the problem of timely exchange of updates between a central station and a set of ground terminals V , via a mobile agent that traverses across the ground terminals along a mobility graph G = (V, E). We design the trajectory of the mobile agent to minimize peak and average age of information (AoI), two newly proposed metrics for measuring timeliness of information. We consider randomized trajectories, in which the mobile agent travels from terminal i to terminal j with probability Pi,j. For the information gathering problem, we show that a randomized trajectory is peak age optimal and factor-8H average age optimal, where H is the mixing time of the randomized trajectory on the mobility graph G. We also show that the average age minimization problem is NP-hard. For the information dissemination problem, we prove that the same randomized trajectory is factor-O(H) peak and average age optimal. Moreover, we propose an age-based trajectory, which utilizes information about current age at terminals, and show that it is factor-2 average age optimal in a symmetric setting.

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“…Closer to our work are [13] and [14], in which some approximation trajectories to minimize maximum latency on metric graphs were proposed. In [15], the authors consider trajectory planning for a mobile agent to minimize AoI.…”

Section: Introductionmentioning

confidence: 98%

Age Optimal Information Gathering and Dissemination on Graphs

Tripathi

¹

,

Talak

²

,

Modiano

³

2019

IEEE INFOCOM 2019 - IEEE Conference on Computer Communications

View full text Add to dashboard Cite

We consider the problem of timely exchange of updates between a central station and a set of ground terminals V , via a mobile agent that traverses across the ground terminals along a mobility graph G = (V, E). We design the trajectory of the mobile agent to minimize peak and average age of information (AoI), two newly proposed metrics for measuring timeliness of information. We consider randomized trajectories, in which the mobile agent travels from terminal i to terminal j with probability Pi,j. For the information gathering problem, we show that a randomized trajectory is peak age optimal and factor-8H average age optimal, where H is the mixing time of the randomized trajectory on the mobility graph G. We also show that the average age minimization problem is NP-hard. For the information dissemination problem, we prove that the same randomized trajectory is factor-O(H) peak and average age optimal. Moreover, we propose an age-based trajectory, which utilizes information about current age at terminals, and show that it is factor-2 average age optimal in a symmetric setting.The authors are with the

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Min-Max Latency Walks: Approximation Algorithms for Monitoring Vertex-Weighted Graphs

Cited by 4 publications

References 17 publications

Persistent monitoring in discrete environments: Minimizing the maximum weighted latency between observations

Persistent monitoring in discrete environments: Minimizing the maximum weighted latency between observations

Age Optimal Information Gathering and Dissemination on Graphs

Age Optimal Information Gathering and Dissemination on Graphs

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