Considering a network with n nodes, where each node initially votes for one (or more) choices out of K possible choices, we present a Distributed Multi-choice Voting/Ranking (DMVR) algorithm to determine either the choice with maximum vote (the voting problem) or to rank all the choices in terms of their acquired votes (the ranking problem). The algorithm consolidates node votes across the network by updating the states of interacting nodes using two key operations; the union and the intersection. The proposed algorithm is simple, independent from network size, and easily scalable in terms of the number of choices K, using only K ×2 K−1 nodal states for voting, and K ×K! nodal states for ranking. We prove the number of states to be optimal in the ranking case; this optimality is conjectured to also apply to the voting case. The time complexity of the algorithm is analyzed in complete graphs. We show that the time complexity for both ranking and voting is O(log(n)) for given vote percentages, and is inversely proportional to the minimum of the vote percentage differences among various choices.

No abstract

We consider a multi-hop switched network operating under a Max-Weight (MW) scheduling policy, and show that the distance between the queue length process and a fluid solution remains bounded by a constant multiple of the deviation of the cumulative arrival process from its average. We then exploit this result to prove matching upper and lower bounds for the time scale over which additive state space collapse (SSC) takes place. This implies, as two special cases, an additive SSC result in diffusion scaling under non-Markovian arrivals and, for the case of i.i.d. arrivals, an additive SSC result over an exponential time scale. * A. Sharifnassab and S. J. Golestani are with the

We consider a class of continuous-time hybrid dynamical systems that correspond to subgradient flows of a piecewise linear and convex potential function with finitely many pieces, and which include the fluid-level dynamics of the Max-Weight scheduling policy as a special case. We study the effect of an external disturbance/perturbation on the state trajectory, and establish that the magnitude of this effect can be bounded by a constant multiple of the integral of the perturbation. † A. Sharifnassab and S. J. Golestani are with the

No abstract