skip to main content

Title: Hop-constrained oblivious routing
We prove the existence of an oblivious routing scheme that is poly(logn)-competitive in terms of (congestion + dilation), thus resolving a well-known question in oblivious routing. Concretely, consider an undirected network and a set of packets each with its own source and destination. The objective is to choose a path for each packet, from its source to its destination, so as to minimize (congestion + dilation), defined as follows: The dilation is the maximum path hop-length, and the congestion is the maximum number of paths that include any single edge. The routing scheme obliviously and randomly selects a path for each packet independent of (the existence of) the other packets. Despite this obliviousness, the selected paths have (congestion + dilation) within a poly(logn) factor of the best possible value. More precisely, for any integer hop-bound h, this oblivious routing scheme selects paths of length at most h · poly(logn) and is poly(logn)-competitive in terms of congestion in comparison to the best possible congestion achievable via paths of length at most h hops. These paths can be sampled in polynomial time. This result can be viewed as an analogue of the celebrated oblivious routing results of R'acke [FOCS 2002, STOC 2008], which are O(logn)-competitive in terms of congestion, but are not competitive in terms of dilation.  more » « less
Award ID(s):
1910588 1814603 1750808 1618280 1527110
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Symposium on Theory of Computing (STOC)
Page Range / eLocation ID:
1208 to 1220
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    The Jellyfish network has recently been proposed as an alternative to the fat-tree network for data centers and high-performance computing clusters. Jellyfish uses a random regular graph as its switch-level topology and has shown to be more cost-effective than fat-trees. Effective routing on Jellyfish is challenging. It is known that shortest path routing and equal cost multi-path routing (ECMP) do not work well on Jellyfish. Existing schemes use variations of k-shortest path routing (KSP). In this work, we study two routing components for Jellyfish: path selection that decides the paths to route traffic, and routing mechanisms that decide which path to be used for each packet. We show that the performance of the existing KSP can be significantly improved by incorporating two heuristics, randomization and edge-disjointness. We evaluate a range of routing mechanisms, including traffic oblivious and traffic adaptive schemes, and identify an adaptive routing scheme with noticeably higher performance than others. 
    more » « less
  2. A Mobile Ad-hoc Network (MANET) is a collection of nodes that communicate with each other wirelessly without any central support or conventional structure. The transmission of data packets over wireless channels in MANETs helps to maintain communication. Ad-hoc On-Demand Distance Vector Routing is a reactive routing protocol associated with MANET which creates a route to destination by broadcasting route request packets through the entire network. A link failure in this type of protocol causes the source to flood the network with these Route Request packets that leads to congestion in the network and performance degradation. This paper proposes an Efficient Multipath AODV routing algorithm that determines if a node in a network is relaying or is silent in the process of route discovery to send data packets from the source to destination. Simulation results show the proposed routing algorithm controls congestion and enhances performance in the network as not all network nodes have to participate in the route discovery for a particular source-destination pair. 
    more » « less
  3. Routing solutions for multi-hop underwater wireless sensor networks suffer significant performance degradation as they fail to adapt to the overwhelming dynamics of underwater environments. To respond to this challenge, we propose a new data forwarding scheme where relay selection swiftly adapts to the varying conditions of the underwater channel. Our protocol, termed CARMA for Channel-aware Reinforcement learning-based Multi-path Adaptive routing, adaptively switches between single-path and multi-path routing guided by a distributed reinforcement learning framework that jointly optimizes route-long energy consumption and packet delivery ratio. We compare the performance of CARMA with that of three other routing solutions, namely, CARP, QELAR and EFlood, through SUNSET-based simulations and experiments at sea. Our results show that CARMA obtains a packet delivery ratio that is up to 40% higher than that of all other protocols. CARMA also delivers packets significantly faster than CARP, QELAR and EFlood, while keeping network energy consumption at bay. 
    more » « less
  4. Oblivious routing has a long history in both the theory and practice of networking. In this work we initiate the formal study of oblivious routing in the context of reconfigurable networks, a new architecture that has recently come to the fore in datacenter networking. These networks allow a rapidly changing bounded-degree pattern of interconnections between nodes, but the network topology and the selection of routing paths must both be oblivious to the traffic demand matrix. Our focus is on the trade-off between maximizing throughput and minimizing latency in these networks. For every constant throughput rate, we characterize (up to a constant factor) the minimum latency achievable by an oblivious reconfigurable network design that satisfies the given throughput guarantee. The trade-off between these two objectives turns out to be surprisingly subtle: the curve depicting it has an unexpected scalloped shape reflecting the fact that load-balancing becomes more difficult when the average length of routing paths is not an integer because equalizing all the path lengths is not possible. The proof of our lower bound uses LP duality to verify that Valiant load balancing is the most efficient oblivious routing scheme when used in combination with an optimally-designed reconfigurable network topology. The proof of our upper bound uses an algebraic construction in which the network nodes are identified with vectors over a finite field, the network topology is described by either the elementary basis or a sequence of Vandermonde matrices, and routing paths are constructed by selecting columns of these matrices to yield the appropriate mixture of path lengths within the shortest possible time interval. 
    more » « less
  5. We present the first all-optical network, Baldur, to enable power-efficient and high-speed communications in future exascale computing systems. The essence of Baldur is its ability to perform packet routing on-the-fly in the optical domain using an emerging technology called the transistor laser (TL), which presents interesting opportunities and challenges at the system level. Optical packet switching readily eliminates many inefficiencies associated with the crossings between optical and electrical domains. However, TL gates consume high power at the current technology node, which makes TL-based buffering and optical clock recovery impractical. Consequently, we must adopt novel (bufferless and clock-less) architecture and design approaches that are substantially different from those used in current networks. At the architecture level, we support a bufferless design by turning to techniques that have fallen out of favor for current networks. Baldur uses a low-radix, multi-stage network with a simple routing algorithm that drops packets to handle congestion, and we further incorporate path multiplicity and randomness to minimize packet drops. This design also minimizes the number of TL gates needed in each switch. At the logic design level, a non-conventional, length-based data encoding scheme is used to eliminate the need for clock recovery. We thoroughly validate and evaluate Baldur using a circuit simulator and a network simulator. Our results show that Baldur achieves up to 3,000X lower average latency while consuming 3.2X-26.4X less power than various state-of-the art networks under a wide variety of traffic patterns and real workloads, for the scale of 1,024 server nodes. Baldur is also highly scalable, since its power per node stays relatively constant as we increase the network size to over 1 million server nodes, which corresponds to 14.6X-31.0X power improvements compared to state-of-the-art networks at this scale. 
    more » « less