Designing Connected Tours That Almost Cover a Network

We consider the problem of planning a set of tours (closed paths) through a network such that every node is at most l-hops away from at least one tour, and all tours are connected. A set of tours is called connected in this work, if there exists a path between any two nodes on the tour that is completely within the set of tours. In other words, in a connected set of of tours, we do not have to leave the tour to travel between any two tour nodes. The problem naturally involves steps related to finding extended dominating sets, travelling salesman tours and forwarding trees such that the cost of data gathering is minimized. We propose a heuristic for this problem that considers the as costs the tour length, and the multi-hop forwarding traffic. We evaluate experimentally the new heuristic for various settings, and also compare against previously proposed approaches for related data gathering problems.