Berthold Vöcking

Exploiting locality for data management in systems of limited bandwidth

This paper deals with data management in computer systems in which the computing nodes are connected by a relatively sparse network. We consider the problem of placing and accessing a set of shared objects that are read and written from the nodes in the network. These objects are, e.g., global variables in a parallel program, pages or cache lines in a virtual shared memory system, shared files in a distributed file system, or pages in the World Wide Web. A data management strategy consists of a placement strategy that maps the objects (possibly dynamically and with redundancy) to the nodes, and an access strategy that describes how reads and writes are handled by the system (including the routing). We investigate static and dynamic data management strategies.

Universal algorithms for store-and-forward and wormhole routing

In this paper we present routing algorithms that are tmiversal in the sense that they route messages along arbitrary (simple) paths in arbitrary networks. The algorithms are analyzed in terms of the number of messages being routed, the maximum number of messages that must cross any edge in the network (edge congestion), the maximum number of edges that a message must cross (dilation), the bufler size, and the bandwidth of the links. We present two main results, both of which have applications to ttnivexsal storeand-forwwd routing and universal wormhole routing. Our results yield significant performance improvements over all previously known universal routing algorithms for a wide range of parameters, and they even improve many time bounds for standard networks. In addition, we present adaptations of our main results for routing along shortest paths in arbitrary networks, and for routing in leveled networks, node-symmetric networks, edge-symmetric networks, expanders, butterflies, and meshes.

A packet routing protocol for arbitrary networks

In this paper, we introduce an on-line protocol which routes any set of packets along shortest paths through an arbitrary N-node network in O(congestion+diameter+log N) rounds, with high probability. This time bound is optimal up to the additive log N, and it was previously only reached for bounded-degree levelled networks.

Universal continuous routing strategies

We analyze universal routing protocols, that is, protocols that can be used for any communication pattern in any network, under a stochastic model of continuous message generation. In particular, we present two universal protocols, a store-and-forward and a wormhole routing protocol, and characterize their performance by the following three parameters: the maximum message generation rate for which the protocol is stable, the expected delay of a message from generation to service, and the time the protocol needs to recover from worst-case scenarios. Both protocols yield significant performance improvements over all previously known continuous routing protocols. In addition, we present adaptations of our protocols to continuous routing in node-symmetric networks, butterflies, and meshes.

Randomized protocols for low-congestion circuit routing in multistage interconnection networks

In this paper we study randomized algorithms for circuit switching on multistage networks related to the butterfly. We devise algorithms that route messages by constructing circuits (or paths) for the messages with small congestion, dilation, and setup time. Our algorithms are based on the idea of having each message choose a route from two possibilities, a technique that has previously proven successful in simpler load balancing settings. As an application of our techniques, we propose a novel design for a data server.

Shortest-Path Routing in Arbitrary Networks

We introduce an on-line protocol which routes any set ofNpackets along shortest paths with congestionCand dilationDthrough an arbitrary network inO(C+D+logN) steps, with high probability. This time bound is optimal up to the additive logN, and it has previously only been reached for bounded-degree leveled networks.Further, we show that the preceding bound holds also for random routing problems withCdenoting the maximum expected congestion over all links. Based on this result, we give applications for random routing in Cayley networks, general node symmetric networks, edge symmetric networks, and de Bruijn networks.Finally, we examine the problems arising when our approach is applied to routing along non-shortest paths, deterministic routing, or routing with bounded buffers.

Approximating Multicast Congestion

We present a randomized algorithm for approximating multicast congestion (a generalization of path congestion) to within O(log n) times the best possible. Our main tools are a linear programming relaxation and iterated randomized rounding.

From static to dynamic routing: efficient transformations of store-and-forward protocols

We investigate how static store-and-forward routing algorithms can be transformed into efficient dynamic algorithms, that is, how algorithms that have been designed for the case that all packets are injected at the same time can be adapted to more realistic scenarios in which packets are continuously injected into the network. Besides describing specific transformations for well-known static routing algorithms, we present a black box transformation scheme applicable to every static, oblivious routing algorithm. We analyze the performance of our protocols under a stochastic and an adversarial model of packet injections. One result of our specific transformations is the first dynamic routing algorithm for leveled networks that is stable for arbitrary admissible injection rates and that works with packet buffers of size depending solely on the injection rate and the node degree, but not on the size of the network. Furthermore, we prove strong delay bounds for the packets. Our results imply, for example, that a throughput of 99% can be achieved on an n-input butterfly network with buffers of constant size while each packet is delivered in time O(log n), with high probability. Our black box transformation ensures that if the static algorithm is pure (i.e., no extra packets apart from the original packets are routed), its dynamic variant is stable up to a maximum possible injection rate. Furthermore, in the stochastic model, the routing time of a packet depends on local parameters such as the length of its routing path, rather than on the maximum possible path length, even if the static algorithm chosen for the transformation does not provide this locality feature and is not pure. In the adversarial model, the delay bound of the packets is closely related to the time bound given for the static algorithm.

Provably Good and Practical Strategies for Non-Uniform Data Management in Networks

This paper deals with the on-line allocation of shared data objects to the local memory modules of the nodes in a network. We assume that the data is organized in indivisible objects such as files, pages, or global variables. The data objects can be replicated and discarded over time in order to minimize the communication load for read and write accesses done by the nodes in the network. Non-uniform data management is characterized by a different communication load for accesses to small pieces of the data objects and migrations of whole data objects.We introduce on-line algorithms that minimize the congestion, i.e., the maximum communication load over all links. Our algorithms are evaluated in a competitive analysis comparing the congestion produced by an on-line algorithm with the congestion produced by an optimal off-line algorithm.We present the first deterministic and distributed algorithm that achieves a constant competitive ratio on trees. Our algorithm minimizes not only the congestion but minimizes simultaneously the load on each individual edge up to a optimal factor of 3.Algorithms for trees are of special interest as they can be used as a subroutine in algorithms for other networks. For example, using our tree algorithm as a subroutine in the recently introduced access tree strategy yields an algorithm that is O(d ? logn)-competitive for d-dimensional meshes with n nodes. This competitive ratio is known to be optimal for meshes of constant dimension.

Data management in networks: experimental evaluation of a provably good strategy

This paper deals with data management for parallel and distributed systems. We present the DIVA (Distributed Variables ) library that provides direct access to shared data objects from each node in a network. The current implementations are based on mesh-connected massively parallel computers. Our algorithms dynamically create and discard copies of the data objects in order to reduce the communication overhead. We use a non-standard approach based on a randomized but locality preserving embedding of ``access trees into the network.