Submodular maximization has been widely used in many multi-robot task planning problems including information gathering, exploration, and target tracking. However, the interplay between submodular maximization and communication is rarely explored in the multi-robot setting. In many cases, maximizing the submodular objective may drive the robots in a way so as to disconnect the communication network. Driven by such observations, in this paper, we consider the problem of maximizing submodular function with connectivity constraints. Specifically, we propose a problem called Communication-aware Submodular Maximization (CSM), in which communication maintenance and submodular maximization are jointly considered in the decision-making process. One heuristic algorithm that consists of two stages, i.e. topology generation and deviation minimization is proposed. We validate the formulation and algorithm through numerical simulation. We find that our algorithm on average suffers only slightly performance decrease compared to the pure greedy strategy.

Given a set of obstacles in 2D or 3D space, a set of n candidate locations where facilities can be established, the Maximum Visibility Facility Selection (MVFS) query finds k out of the n locations, that yield the maximum visibility coverage of the data space. Though the MVFS problem has been extensively studied in visual sensor networks, computational geometry, and computer vision in the form of optimal camera placement problem, existing solutions are designed for discretized space and only work for MVFS instances having a few hundred facilities. In this paper, we revisit the MVFS problem to support new spatial database applications like "where to place security cameras to ensure better surveillance of a building complex?" or "where to place billboards in the city to maximize visibility from the surrounding space?". We introduce the concept of equivisibility triangulation to devise the first approach to accurately determine the visibility coverage of continuous data space from a subset of the facility locations, which avoids the limitations of discretizing the data space. Then, we propose an efficient graph-theoretic approach that exploits the idea of vertex separators for efficient exact in-memory solution of the MVFS problem. Finally, we propose the first external-memory based approximation algorithm (with a guaranteed approximation ratio of 1 - 1/e) that is scalable for a large number of obstacles and facility locations. We conduct extensive experimental study to show the effectiveness and efficiency of our proposed algorithms.