Routing in random ad-hoc networks: provably better than worst-case

Wireless networks, such as sensor networks or general ad-hoc networks, present special challenges for routing problems due to high energy constraints, failures, and node autonomy. As such, traditional methods of constructing and fixing a centralized routing topology and then simply expecting nodes to forward accordingly in the absence of any further incentives to do so suffer reliability drawbacks. We look to light-weight and game-theoretic proposals based on random walks and game-theoretic techniques to deal with these reliability concerns. In particular, we consider random walks for information collection, path auctions for one-to-one routing, and a locally minimum cost forwarding game (LMCF) for all-to-one reverse multicast routing. For each of the three routing scenarios considered, a trade-off between reliability and efficiency is observed in the worst-cases: There exist wireless network configurations for which random walks take a maximally long expected time to visit all nodes, path auctions require maximal overpayments to ensure truthfulness, and any Nash equilibria for locally minimum cost forwarding are arbitrarily costlier than the global optimum. We further demonstrate NP-hardness results and approximation hardness results regarding computation of optimal truthful mechanisms and optimal Nash equilibria for the game-theoretic scenarios present. On the other hand, a clique is also a possible wireless network configuration formed by setting a large enough (broadcast radius, and the clique configuration demonstrates optimal efficiency for all three. The extreme downside to such a configuration, however, is that such a large broadcast radius would rapidly deplete the system's energy, yielding it completely infeasible. What becomes apparent then, is that the appropriate question to ask is the following: What is the efficiency of each of the three proposed methods for a typical wireless network of low broadcast radius'? Does a nicer structure tend to arise despite negative worst-case behavior for the reliable routing problems considered in this work on the relevant random models of wireless networks'? A central theme of this work is a resounding, theoretically sound "Yes" to that question for all three scenarios: We prove that each of the three proposed methods are almost always efficient under relevant, models and metrics models for wireless networks.