Lower Bounds for Structuring Unreliable Radio Networks

In this paper, we study lower bounds for randomized solutions to the maximal independent set (MIS) and connected dominating set (CDS) problems in the dual graph model of radio networks---a generalization of the standard graph-based model that now includes unreliable links controlled by an adversary. We begin by proving that a natural geographic constraint on the network topology is required to solve these problems efficiently (i.e., in time polylogarthmic in the network size). We then prove the importance of the assumption that nodes are provided advance knowledge of their reliable neighbors (i.e, neighbors connected by reliable links). Combined, these results answer an open question by proving that the efficient MIS and CDS algorithms from [Censor-Hillel, PODC 2011] are optimal with respect to their dual graph model assumptions. They also provide insight into what properties of an unreliable network enable efficient local computation.Comment: An extended abstract of this work appears in the 2014 proceedings of the International Symposium on Distributed Computing (DISC

Connected Coordination: Network Structure and Group Coordination

Networks can affect a group’s ability to solve a coordination problem. We utilize laboratory experiments to study the conditions under which groups of subjects can solve coordination games. We investigate a variety of different network structures, and we also investigate coordination games with symmetric and asymmetric payoffs. Our results show that network connections facilitate coordination in both symmetric and asymmetric games. Most significantly, we find that increases in the number of network connections encourage coordination even when payoffs are highly asymmetric. These results shed light on the conditions that may facilitate coordination in real-world networks

Strong Structural Controllability of Signed Networks

In this paper, we discuss the controllability of a family of linear time-invariant (LTI) networks defined on a signed graph. In this direction, we introduce the notion of positive and negative signed zero forcing sets for the controllability analysis of positive and negative eigenvalues of system matrices with the same sign pattern. A sufficient combinatorial condition that ensures the strong structural controllability of signed networks is then proposed. Moreover, an upper bound on the maximum multiplicity of positive and negative eigenvalues associated with a signed graph is provided

Communication Primitives in Cognitive Radio Networks

Cognitive radio networks are a new type of multi-channel wireless network in which different nodes can have access to different sets of channels. By providing multiple channels, they improve the efficiency and reliability of wireless communication. However, the heterogeneous nature of cognitive radio networks also brings new challenges to the design and analysis of distributed algorithms. In this paper, we focus on two fundamental problems in cognitive radio networks: neighbor discovery, and global broadcast. We consider a network containing $n$ nodes, each of which has access to $c$ channels. We assume the network has diameter $D$, and each pair of neighbors have at least $k\geq 1$, and at most $k_{max}\leq c$, shared channels. We also assume each node has at most $\Delta$ neighbors. For the neighbor discovery problem, we design a randomized algorithm CSeek which has time complexity $\tilde{O}((c^2/k)+(k_{max}/k)\cdot\Delta)$. CSeek is flexible and robust, which allows us to use it as a generic "filter" to find "well-connected" neighbors with an even shorter running time. We then move on to the global broadcast problem, and propose CGCast, a randomized algorithm which takes $\tilde{O}((c^2/k)+(k_{max}/k)\cdot\Delta+D\cdot\Delta)$ time. CGCast uses CSeek to achieve communication among neighbors, and uses edge coloring to establish an efficient schedule for fast message dissemination. Towards the end of the paper, we give lower bounds for solving the two problems. These lower bounds demonstrate that in many situations, CSeek and CGCast are near optimal