arXiv subjects

P. Brighten Godfrey

Publications and source records attributed to P. Brighten Godfrey.

25 records · Page 2Linked to original sources

arXiv2012

Shortest Paths in Less Than a Millisecond

We consider the problem of answering point-to-point shortest path queries on massive social networks. The goal is to answer queries within tens of milliseconds while minimizing the memory requirements. We present a technique that achieves this goal for an extremely large fraction of path queries by exploiting the structure of the social networks. Using evaluations on real-world datasets, we argue that our technique offers a unique trade-off between latency, memory and accuracy. For instance, for the LiveJournal social network (roughly 5 million nodes and 69 million edges), our technique can answer 99.9% of the queries in less than a millisecond. In comparison to storing all pair shortest paths, our technique requires at least 550x less memory; the average query time is roughly 365 microseconds --- 430x faster than the state-of-the-art shortest path algorithm. Furthermore, the relative performance of our technique improves with the size (and density) of the network. For the Orkut social network (3 million nodes and 220 million edges), for instance, our technique is roughly 2588x faster than the state-of-the-art algorithm for computing shortest paths.

cs.SI↗

arXiv2012

Jellyfish: Networking Data Centers Randomly

Industry experience indicates that the ability to incrementally expand data centers is essential. However, existing high-bandwidth network designs have rigid structure that interferes with incremental expansion. We present Jellyfish, a high-capacity network interconnect, which, by adopting a random graph topology, yields itself naturally to incremental expansion. Somewhat surprisingly, Jellyfish is more cost-efficient than a fat-tree: A Jellyfish interconnect built using the same equipment as a fat-tree, supports as many as 25% more servers at full capacity at the scale of a few thousand nodes, and this advantage improves with scale. Jellyfish also allows great flexibility in building networks with different degrees of oversubscription. However, Jellyfish's unstructured design brings new challenges in routing, physical layout, and wiring. We describe and evaluate approaches that resolve these challenges effectively, indicating that Jellyfish could be deployed in today's data centers.

cs.NI↗

arXiv2012

Faster Approximate Distance Queries and Compact Routing in Sparse Graphs

A distance oracle is a compact representation of the shortest distance matrix of a graph. It can be queried to approximate shortest paths between any pair of vertices. Any distance oracle that returns paths of worst-case stretch (2k-1) must require space $Ω(n^{1 + 1/k})$ for graphs of n nodes. The hard cases that enforce this lower bound are, however, rather dense graphs with average degree Ω(n^{1/k}). We present distance oracles that, for sparse graphs, substantially break the lower bound barrier at the expense of higher query time. For any 1 \leq α\leq n, our distance oracles can return stretch 2 paths using O(m + n^2/α) space and stretch 3 paths using O(m + n^2/α^2) space, at the expense of O(αm/n) query time. By setting appropriate values of α, we get the first distance oracles that have size linear in the size of the graph, and return constant stretch paths in non-trivial query time. The query time can be further reduced to O(α), by using an additional O(m α) space for all our distance oracles, or at the cost of a small constant additive stretch. We use our stretch 2 distance oracle to present the first compact routing scheme with worst-case stretch 2. Any compact routing scheme with stretch less than 2 must require linear memory at some nodes even for sparse graphs; our scheme, hence, achieves the optimal stretch with non-trivial memory requirements. Moreover, supported by large-scale simulations on graphs including the AS-level Internet graph, we argue that our stretch-2 scheme would be simple and efficient to implement as a distributed compact routing protocol.

cs.DS↗

arXiv2012

Slick Packets

Source-controlled routing has been proposed as a way to improve flexibility of future network architectures, as well as simplifying the data plane. However, if a packet specifies its path, this precludes fast local re-routing within the network. We propose SlickPackets, a novel solution that allows packets to slip around failures by specifying alternate paths in their headers, in the form of compactly-encoded directed acyclic graphs. We show that this can be accomplished with reasonably small packet headers for real network topologies, and results in responsiveness to failures that is competitive with past approaches that require much more state within the network. Our approach thus enables fast failure response while preserving the benefits of source-controlled routing.

cs.NI↗

arXiv2011

BGP Stability is Precarious

We note a fact which is simple, but may be useful for the networking research community: essentially any change to BGP's decision process can cause divergence --- or convergence when BGP would otherwise diverge.

cs.NI↗

arXiv2008

Network Coding for Distributed Storage Systems

Distributed storage systems provide reliable access to data through redundancy spread over individually unreliable nodes. Application scenarios include data centers, peer-to-peer storage systems, and storage in wireless networks. Storing data using an erasure code, in fragments spread across nodes, requires less redundancy than simple replication for the same level of reliability. However, since fragments must be periodically replaced as nodes fail, a key question is how to generate encoded fragments in a distributed way while transferring as little data as possible across the network. For an erasure coded system, a common practice to repair from a node failure is for a new node to download subsets of data stored at a number of surviving nodes, reconstruct a lost coded block using the downloaded data, and store it at the new node. We show that this procedure is sub-optimal. We introduce the notion of regenerating codes, which allow a new node to download \emph{functions} of the stored data from the surviving nodes. We show that regenerating codes can significantly reduce the repair bandwidth. Further, we show that there is a fundamental tradeoff between storage and repair bandwidth which we theoretically characterize using flow arguments on an appropriately constructed graph. By invoking constructive results in network coding, we introduce regenerating codes that can achieve any point in this optimal tradeoff.

cs.NI↗

arXiv2007

Network Coding for Distributed Storage Systems

Peer-to-peer distributed storage systems provide reliable access to data through redundancy spread over nodes across the Internet. A key goal is to minimize the amount of bandwidth used to maintain that redundancy. Storing a file using an erasure code, in fragments spread across nodes, promises to require less redundancy and hence less maintenance bandwidth than simple replication to provide the same level of reliability. However, since fragments must be periodically replaced as nodes fail, a key question is how to generate a new fragment in a distributed way while transferring as little data as possible across the network. In this paper, we introduce a general technique to analyze storage architectures that combine any form of coding and replication, as well as presenting two new schemes for maintaining redundancy using erasure codes. First, we show how to optimally generate MDS fragments directly from existing fragments in the system. Second, we introduce a new scheme called Regenerating Codes which use slightly larger fragments than MDS but have lower overall bandwidth use. We also show through simulation that in realistic environments, Regenerating Codes can reduce maintenance bandwidth use by 25 percent or more compared with the best previous design--a hybrid of replication and erasure codes--while simplifying system architecture.

cs.IT↗