Distributed Algorithm for Solving the Bottleneck Assignment Problem

Khoo, Mitchell; Wood, Tony; Manzie, Chris; Shames, Iman

doi:10.1109/cdc40024.2019.9028897

Cited by 6 publications

(16 citation statements)

References 26 publications

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“…Finding the k-th order bottleneck and the corresponding robustness margin requires solving two BAPs that can each be computed with a complexity of O(| Ēk || Tk |), see [8]. From (8)…”

Section: B Sequential Bottleneck Assignmentmentioning

confidence: 99%

“…Remark 1: The algorithm introduced in [8] solves the BAP without centralised decision making. Agents only have knowledge of weights associated to them, i.e., agent i ∈ A has access to the subset of weights W i := {w i,j | j ∈ T }, and communicates local estimates of maximal and minimal edge weights to other agents.…”

Section: B Sequential Bottleneck Assignmentmentioning

confidence: 99%

“…We note that (i ′ , j * a ) ∈ Ēa by definition in (8). Because (i ′ , j * a ) is not assigned according Π * , it follows from Definition 4 that w i ′ ,j *…”

Section: Appendix III Proof Of Propositionmentioning

confidence: 99%

“…A review of the state-of-the-art methods to solve the BAP is provided in [5]. In [8] an algorithm to solve the BAP with distributed computation is introduced. The sensitivity of the bottleneck optimising assignment with respect to changes in the assignment costs is investigated in [9].…”

Section: Introductionmentioning

confidence: 99%

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Collision Avoidance Based on Robust Lexicographic Task Assignment

Wood,

Khoo,

Michael

et al. 2020

Preprint

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Traditional task assignment approaches for multiagent motion control do not take the possibility of collisions into account. This can lead to challenging requirements for the path planning and guidance of the individual agents. To address this issue, we derive an assignment method that not only minimises the largest distance between an agent and its assigned destination but also provides local constraints for guaranteed collision avoidance. To this end, we introduce a sequential bottleneck assignment problem and define a notion of robustness of an optimal assignment. Conditioned on a sufficient level of robustness in relation to the size of the agents, we construct local time-varying position bounds for every individual agent. These local constraints are a direct byproduct of the assignment procedure and only depend on the initial agent positions, the locations that are to be visited, and a timing parameter. We show that no agent that is assigned to move to one of the target destinations collides with any other agent if all agents satisfy their local position constraints. We demonstrate the applicability of the method in a numerical case study.

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“…Finding the k-th order bottleneck and the corresponding robustness margin requires solving two BAPs that can each be computed with a complexity of O(| Ēk || Tk |), see [8]. From (8)…”

Section: B Sequential Bottleneck Assignmentmentioning

confidence: 99%

Section: B Sequential Bottleneck Assignmentmentioning

confidence: 99%

“…We note that (i ′ , j * a ) ∈ Ēa by definition in (8). Because (i ′ , j * a ) is not assigned according Π * , it follows from Definition 4 that w i ′ ,j *…”

Section: Appendix III Proof Of Propositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Collision Avoidance Based on Robust Lexicographic Task Assignment

Wood,

Khoo,

Michael

et al. 2020

Preprint

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“…In contrast, a distributed algorithm is one where computation is distributed over agents. Several centralised algorithms to solve the BAP have been proposed in [5,6,7,8], while a distributed algorithm to solve the BAP is presented in [9].…”

Section: Introductionmentioning

confidence: 99%

A Greedy and Distributable Approach to the Lexicographic Bottleneck Assignment Problem with Conditions on Exactness

Khoo¹,

Wood²,

Manzie³

et al. 2020

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The Lexicographical Bottleneck Assignment Problem (LexBAP) typically requires centralised computation with ( 4 ) complexity. We consider the Sequential Bottleneck Assignment Problem (Se-qBAP) and its relationship to the LexBAP. By exploiting structure of the Bottleneck Assignment Problem, we derive an algorithm that solves the SeqBAP with ( 3 ) complexity. We analyse conditions for which solutions sets of the LexBAP and the SeqBAP coincide. When these conditions hold, the algorithm solves the LexBAP with computation that can be distributed over a network of agents.

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