Compact Oblivious Routing

Oblivious routing is an attractive paradigm for large distributed systems in which centralized control and frequent reconfigurations are infeasible or undesired (e.g., costly). Over the last almost 20 years, much progress has been made in devising oblivious routing schemes that guarantee close to optimal load and also algorithms for constructing such schemes efficiently have been designed. However, a common drawback of existing oblivious routing schemes is that they are not compact: they require large routing tables (of polynomial size), which does not scale. This paper presents the first oblivious routing scheme which guarantees close to optimal load and is compact at the same time - requiring routing tables of polylogarithmic size. Our algorithm maintains the polylogarithmic competitive ratio of existing algorithms, and is hence particularly well-suited for emerging large-scale networks

Compact routing in fault-tolerant distributed systems

A compact routing algorithm is a routing algorithm which reduces the space complexity of all-pairs shortest path routing. Compact routing protocols in distributed systems have been studied extensively as an attractive alternative to the traditional method of all-pairs shortest path routing. The use of compact routing protocols have several advantages. Compact routing schemes are not only more memory-efficient, but provide faster routing table lookup, more efficient broadcast scheme, and allow for a more scalable network. These routing schemes still maintain optimal or near-optimal routing paths. However, most of the compact routing protocols are not fault-tolerant. This thesis will first report the recent developments in the compact routing research. Several new methods for compact routing in fault-tolerant distributed systems will be presented and analyzed. The most important feature of the algorithms presented in this thesis is that they are self-stabilizing. The self-stabilization paradigm has been shown to be the most unified and all-inclusive approach to the design of fault-tolerant system. Additionally, these algorithms will address and solve several problems left unsolved by previous works. Relabelable and non-relabelable networks will be considered for both specific and arbitrary topologies

On Compact Routing for the Internet

While there exist compact routing schemes designed for grids, trees, and Internet-like topologies that offer routing tables of sizes that scale logarithmically with the network size, we demonstrate in this paper that in view of recent results in compact routing research, such logarithmic scaling on Internet-like topologies is fundamentally impossible in the presence of topology dynamics or topology-independent (flat) addressing. We use analytic arguments to show that the number of routing control messages per topology change cannot scale better than linearly on Internet-like topologies. We also employ simulations to confirm that logarithmic routing table size scaling gets broken by topology-independent addressing, a cornerstone of popular locator-identifier split proposals aiming at improving routing scaling in the presence of network topology dynamics or host mobility. These pessimistic findings lead us to the conclusion that a fundamental re-examination of assumptions behind routing models and abstractions is needed in order to find a routing architecture that would be able to scale ``indefinitely.''Comment: This is a significantly revised, journal version of cs/050802

Certification of Compact Low-Stretch Routing Schemes

On the one hand, the correctness of routing protocols in networks is an issue of utmost importance for guaranteeing the delivery of messages from any source to any target. On the other hand, a large collection of routing schemes have been proposed during the last two decades, with the objective of transmitting messages along short routes, while keeping the routing tables small. Regrettably, all these schemes share the property that an adversary may modify the content of the routing tables with the objective of, e.g., blocking the delivery of messages between some pairs of nodes, without being detected by any node. In this paper, we present a simple certification mechanism which enables the nodes to locally detect any alteration of their routing tables. In particular, we show how to locally verify the stretch 3 routing scheme by Thorup and Zwick [SPAA 2001] by adding certificates of ~O(sqrt(n)) bits at each node in n-node networks, that is, by keeping the memory size of the same order of magnitude as the original routing tables. We also propose a new name-independent routing scheme using routing tables of size ~O(sqrt(n)) bits. This new routing scheme can be locally verified using certificates on ~O(sqrt(n)) bits. Its stretch is 3 if using handshaking, and 5 otherwise

Space-Efficient Routing Tables for Almost All Networks and the Incompressibility Method

We use the incompressibility method based on Kolmogorov complexity to determine the total number of bits of routing information for almost all network topologies. In most models for routing, for almost all labeled graphs $\Theta (n^2)$ bits are necessary and sufficient for shortest path routing. By `almost all graphs' we mean the Kolmogorov random graphs which constitute a fraction of $1-1/n^c$ of all graphs on $n$ nodes, where $c > 0$ is an arbitrary fixed constant. There is a model for which the average case lower bound rises to $\Omega(n^2 \log n)$ and another model where the average case upper bound drops to $O(n \log^2 n)$. This clearly exposes the sensitivity of such bounds to the model under consideration. If paths have to be short, but need not be shortest (if the stretch factor may be larger than 1), then much less space is needed on average, even in the more demanding models. Full-information routing requires $\Theta (n^3)$ bits on average. For worst-case static networks we prove a $\Omega(n^2 \log n)$ lower bound for shortest path routing and all stretch factors $<2$ in some networks where free relabeling is not allowed.Comment: 19 pages, Latex, 1 table, 1 figure; SIAM J. Comput., To appea

Using Sphinx to Improve Onion Routing Circuit Construction

This paper presents compact message formats for onion routing circuit construction using the Sphinx methodology developed for mixes. We significantly compress the circuit construction messages for three onion routing protocols that have emerged as enhancements to the Tor anonymizing network; namely, Tor with predistributed Diffie-Hellman values, pairing-based onion routing, and certificateless onion routing. Our new circuit constructions are also secure in the universal composability framework, a property that was missing from the original constructions. Further, we compare the performance of our schemes with their older counterparts as well as with each other

Labeling Schemes with Queries

We study the question of ``how robust are the known lower bounds of labeling schemes when one increases the number of consulted labels''. Let $f$ be a function on pairs of vertices. An $f$-labeling scheme for a family of graphs \cF labels the vertices of all graphs in \cF such that for every graph G\in\cF and every two vertices $u,v\in G$, the value $f(u,v)$ can be inferred by merely inspecting the labels of $u$ and $v$. This paper introduces a natural generalization: the notion of $f$-labeling schemes with queries, in which the value $f(u,v)$ can be inferred by inspecting not only the labels of $u$ and $v$ but possibly the labels of some additional vertices. We show that inspecting the label of a single additional vertex (one {\em query}) enables us to reduce the label size of many labeling schemes significantly