We consider the following matching-based routing problem. Initially, each vertex v of a connected graph G is occupied by pebble which has unique destination $$\pi (v)$$ . In round pebbles across edges selected matching in are swapped, and goal to route its as few rounds possible. show that if sufficiently strong d-regular spectral expander then any permutation $$ can be achieved $$O(\log n)$$ r...

We study path auction games in which multiple edges may be owned by the same agent in this paper. The edge costs and the set of edges owned by the same agent are privately known to the owner of the edge. We show that in this setting, given the assumption the losing agent always has 0 payoff, there is no individual rational strategyproof mechanism in which only edge costs are reported. If the ag...

We prove a Riemann-Roch theorem for real divisors on edgeweighted graphs over the reals, extending the result of Baker and Norine for integral divisors on graphs with multiple edges.

We prove a Riemann-Roch theorem for real divisors on edge-weighted graphs over the reals, extending the result of Baker and Norine for integral divisors on graphs with multiple edges.

We study two types of two player, perfect information games with no chance moves, played on the edge set of the binomial random graph G(n, p). In each round of the (1 : q) Waiter-Client Hamiltonicity game, the first player, called Waiter, offers the second player, called Client, q + 1 edges of G(n, p) which have not been offered previously. Client then chooses one of these edges, which he claim...

For positive integers n and q and a monotone graph property A, we consider the two player, perfect information game WC(n, q,A), which is defined as follows. The game proceeds in rounds. In each round, the first player, called Waiter, offers the second player, called Client, q + 1 edges of the complete graph Kn which have not been offered previously. Client then chooses one of these edges which ...

In a sequence of recent results (PODC 2015 and PODC 2016), the running time of the fastest algorithm for the minimum spanning tree (MST) problem in the Congested Clique model was first improved to O(log log logn) from O(log logn) (Hegeman et al., PODC 2015) and then to O(log∗ n) (Ghaffari and Parter, PODC 2016). All of these algorithms use Θ(n2) messages independent of the number of edges in th...