Fair Surveillance Assignment Problem

Fangxiao Wang, Bo Li

Keywords: Surveillance, Fair Division, Indivisible Chores, Vertex Cover

Abstract:

Monitoring a specific set of locations serves multiple purposes in practice, such as infrastructure inspection and safety surveillance.
We study a generalization of the surveillance problem, where the monitoring area, represented by a graph, is divided and assigned to a set of agents with customized cost functions.
In this paper, each agent's patrolling cost towards receiving a subgraph is quantified by the weight of the minimum vertex cover therein, and our objective is to design algorithms to compute fair assignments of the surveillance tasks.
The fairness is assessed using maximin share (MMS) fairness proposed by Budish [J. Political Econ., 2011].
Our main result is an algorithm which ensures a
$\frac{5+\sqrt{17}}{2}$($\approx 4.562$)-approximate MMS allocation for any number of agents with arbitrary vertex weights.
We then prove that no algorithm can be better than 2-approximate MMS fair.
For scenarios involving no more than four agents, we further improve the approximation ratio to 2, which is thus the optimal achievable ratio.

Track: Economics, Online Markets, and Human Computation

Submission Guidelines Scope: Yes

Submission Guidelines Blind: Yes

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Student Author: Yes

Submission Number: 1795