OutFlank Routing: Increasing Throughput in Toroidal Interconnection Networks

We present a new, deadlock-free, routing scheme for toroidal interconnection networks, called OutFlank Routing (OFR). OFR is an adaptive strategy which exploits non-minimal links, both in the source and in the destination nodes. When minimal links are congested, OFR deroutes packets to carefully chosen intermediate destinations, in order to obtain travel paths which are only an additive constant longer than the shortest ones. Since routing performance is very sensitive to changes in the traffic model or in the router parameters, an accurate discrete-event simulator of the toroidal network has been developed to empirically validate OFR, by comparing it against other relevant routing strategies, over a range of typical real-world traffic patterns. On the 16x16x16 (4096 nodes) simulated network OFR exhibits improvements of the maximum sustained throughput between 14% and 114%, with respect to Adaptive Bubble Routing.Comment: 9 pages, 5 figures, to be presented at ICPADS 201

A note on hierarchical hubbing for a generalization of the VPN problem

Robust network design refers to a class of optimization problems that occur when designing networks to efficiently handle variable demands. The notion of "hierarchical hubbing" was introduced (in the narrow context of a specific robust network design question), by Olver and Shepherd [2010]. Hierarchical hubbing allows for routings with a multiplicity of "hubs" which are connected to the terminals and to each other in a treelike fashion. Recently, Fr\'echette et al. [2013] explored this notion much more generally, focusing on its applicability to an extension of the well-studied hose model that allows for upper bounds on individual point-to-point demands. In this paper, we consider hierarchical hubbing in the context of a previously studied (and extremely natural) generalization of the hose model, and prove that the optimal hierarchical hubbing solution can be found efficiently. This result is relevant to a recently proposed generalization of the "VPN Conjecture".Comment: 14 pages, 1 figur

Near-Optimal Induced Universal Graphs for Bounded Degree Graphs

A graph $U$ is an induced universal graph for a family $F$ of graphs if every graph in $F$ is a vertex-induced subgraph of $U$. For the family of all undirected graphs on $n$ vertices Alstrup, Kaplan, Thorup, and Zwick [STOC 2015] give an induced universal graph with $O\!\left(2^{n/2}\right)$ vertices, matching a lower bound by Moon [Proc. Glasgow Math. Assoc. 1965]. Let $k= \lceil D/2 \rceil$. Improving asymptotically on previous results by Butler [Graphs and Combinatorics 2009] and Esperet, Arnaud and Ochem [IPL 2008], we give an induced universal graph with $O\!\left(\frac{k2^k}{k!}n^k \right)$ vertices for the family of graphs with $n$ vertices of maximum degree $D$. For constant $D$, Butler gives a lower bound of $\Omega\!\left(n^{D/2}\right)$. For an odd constant $D\geq 3$, Esperet et al. and Alon and Capalbo [SODA 2008] give a graph with $O\!\left(n^{k-\frac{1}{D}}\right)$ vertices. Using their techniques for any (including constant) even values of $D$ gives asymptotically worse bounds than we present. For large $D$, i.e. when $D = \Omega\left(\log^3 n\right)$, the previous best upper bound was ${n\choose\lceil D/2\rceil} n^{O(1)}$ due to Adjiashvili and Rotbart [ICALP 2014]. We give upper and lower bounds showing that the size is ${\lfloor n/2\rfloor\choose\lfloor D/2 \rfloor}2^{\pm\tilde{O}\left(\sqrt{D}\right)}$. Hence the optimal size is $2^{\tilde{O}(D)}$ and our construction is within a factor of $2^{\tilde{O}\left(\sqrt{D}\right)}$ from this. The previous results were larger by at least a factor of $2^{\Omega(D)}$. As a part of the above, proving a conjecture by Esperet et al., we construct an induced universal graph with $2n-1$ vertices for the family of graphs with max degree $2$. In addition, we give results for acyclic graphs with max degree $2$ and cycle graphs. Our results imply the first labeling schemes that for any $D$ are at most $o(n)$ bits from optimal

Static virtual channel allocation in oblivious routing

Most virtual channel routers have multiple virtual channels to mitigate the effects of head-of-line blocking. When there are more flows than virtual channels at a link, packets or flows must compete for channels, either in a dynamic way at each link or by static assignment computed before transmission starts. In this paper, we present methods that statically allocate channels to flows at each link when oblivious routing is used, and ensure deadlock freedom for arbitrary minimal routes when two or more virtual channels are available. We then experimentally explore the performance trade-offs of static and dynamic virtual channel allocation for various oblivious routing methods, including DOR, ROMM, Valiant and a novel bandwidth-sensitive oblivious routing scheme (BSORM). Through judicious separation of flows, static allocation schemes often exceed the performance of dynamic allocation schemes