Edge Cloud Computing (ECC) provides a new paradigm for app vendors to serve their users with low latency by deploying their services on edge servers attached to base stations or access points in close proximity to mobile users. From the edge infrastructure provider’s perspective, a cost-effective

$k$

edge server placement (

$k$

ESP) aims to place

$k$

edge servers within a particular geographic area to maximize the number of covered mobile users, i.e., to maximize the user coverage . However, in the distributed and volatile ECC environment, edge servers are subject to failures due to various reasons, e.g., software exceptions, hardware faults, cyberattacks, etc. Mobile users connected to a failed edge server have to access services in the remote cloud if they are not covered by any other edge servers. This significantly impacts mobile users quality of experience. Thus, the robustness of the edge server network (referred to as network robustness hereafter) in a specific area must be considered in edge server placement. In this article, we formally model this joint user coverage and network robustness oriented

$k$

edge server placement (

$k$

ESP-CR) problem, and prove that finding the optimal solution to this problem is

$\mathcal {NP}$

-hard. To tackle this ESP-CR, we first propose an integer programming based optimal approach (namely ESP-O) for finding optimal solutions to small-scale

$k$

ESP-CR problems. Then, we propose an approximation approach, namely ESP-A, for solving large-scale

$k$

ESP-CR problems efficiently and theoretically prove its approximation ratio. Finally, the performance of these two approaches are experimentally evaluated against three representative approaches on a widely-used real-world dataset.

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