Brief Announcement: On Self-Adjusting Skip List Networks

This paper explores the design of dynamic network topologies which adjust to the workload they serve, in an online manner. Such self-adjusting networks (SANs) are enabled by emerging optical technologies, and can be found, e.g., in datacenters. SANs can be used to reduce routing costs by moving frequently communicating nodes topologically closer. This paper presents SANs which provide, for the first time, provable working set guarantees: the routing cost between node pairs is proportional to how recently these nodes communicated last time. Our SANs rely on skip lists (which serve as the topology) and provide additional interesting properties such as local routing

Distributed Computing on Core-Periphery Networks: Axiom-based Design

Inspired by social networks and complex systems, we propose a core-periphery network architecture that supports fast computation for many distributed algorithms and is robust and efficient in number of links. Rather than providing a concrete network model, we take an axiom-based design approach. We provide three intuitive (and independent) algorithmic axioms and prove that any network that satisfies all axioms enjoys an efficient algorithm for a range of tasks (e.g., MST, sparse matrix multiplication, etc.). We also show the minimality of our axiom set: for networks that satisfy any subset of the axioms, the same efficiency cannot be guaranteed for any deterministic algorithm

A note on uniform power connectivity in the SINR model

In this paper we study the connectivity problem for wireless networks under the Signal to Interference plus Noise Ratio (SINR) model. Given a set of radio transmitters distributed in some area, we seek to build a directed strongly connected communication graph, and compute an edge coloring of this graph such that the transmitter-receiver pairs in each color class can communicate simultaneously. Depending on the interference model, more or less colors, corresponding to the number of frequencies or time slots, are necessary. We consider the SINR model that compares the received power of a signal at a receiver to the sum of the strength of other signals plus ambient noise . The strength of a signal is assumed to fade polynomially with the distance from the sender, depending on the so-called path-loss exponent $\alpha$. We show that, when all transmitters use the same power, the number of colors needed is constant in one-dimensional grids if $\alpha>1$ as well as in two-dimensional grids if $\alpha>2$. For smaller path-loss exponents and two-dimensional grids we prove upper and lower bounds in the order of $\mathcal{O}(\log n)$ and $\Omega(\log n/\log\log n)$ for $\alpha=2$ and $\Theta(n^{2/\alpha-1})$ for $\alpha<2$ respectively. If nodes are distributed uniformly at random on the interval $[0,1]$, a \emph{regular} coloring of $\mathcal{O}(\log n)$ colors guarantees connectivity, while $\Omega(\log \log n)$ colors are required for any coloring.Comment: 13 page