Communication complexity

About: Communication complexity is a research topic. Over the lifetime, 3870 publications have been published within this topic receiving 105832 citations.

The Communication Complexity of Pointer Chasing

Abstract: We study the k-round two-party communication complexity of the pointer chasing problem for fixed k. C. Damm, S. Jukna and J. Sgall (1998, Comput. Complexity7, 109?127) showed an upper bound of O(nlog(k?1)n) for this problem. We prove a matching lower bound; this improves the lower bound of ?(n) shown by N. Nisan and A. Widgerson (1993, SIAM J. Comput.22, 211?219), and yields a corresponding improvement in the hierarchy results derived by them and by H. Klauck (1998, in “Proceeding of the Thirteenth Annual IEEE Conference on Computational Complexity,” pp. 141?152) for bounded-depth monotone circuits. We consider the bit version of this problem, and show upper and lower bounds. This implies that there is an abrupt jump in complexity, from linear to superlinear, when the number of rounds is reduced to k/2 or less. We also consider the s-paths version (originally studied by H. Klauck) and show an upper bound. The lower bounds are based on arguments using entropy. One of the main contributions of this work is a transfer lemma for distributions with high entropy; this should be of independent interest.

A Primal-Dual Bicriteria Distributed Algorithm for Capacitated Vertex Cover

Abstract: In this paper we consider the capacitated vertex cover problem, which is the variant of vertex cover where each node is allowed to cover a limited number of edges. We present an efficient, deterministic, distributed approximation algorithm for the problem. Our algorithm computes a $(2+\epsilon)$-approximate solution which violates the capacity constraints by a factor of $(4+\epsilon)$ in a polylogarithmic number of communication rounds. On the other hand, we also show that every efficient distributed approximation algorithm for this problem must violate the capacity constraints. Our result is achieved in two steps. We first develop a $2$-approximate, sequential primal-dual algorithm that violates the capacity constraints by a factor of $2$. Subsequently, we present a distributed version of this algorithm. We demonstrate that the sequential algorithm has an inherent need for synchronization which forces any naive distributed implementation to use a linear number of communication rounds. The challenge in this step is therefore to achieve a reduction of the communication complexity to a polylogarithmic number of rounds without worsening the approximation guarantee.

Hop limited flooding over dynamic networks

Abstract: We study the performance of hop-limited broadcasting of a message in dynamic graphs where links between nodes switch between active and inactive states. We analyze the performance with respect to the completion time, defined as the time for the message to reach a given portion of nodes, and the communication complexity, defined as the number of message forwarding per node. We analyze two natural flooding algorithms. First is a lazy algorithm where the message can be forwarded by a node only if it was first received by this node through a path shorter than the hop limit count. Second is a more complex protocol where each node forwards the message at a given time, if it could have been received by this node through a path shorter than the hop limit count. We derive exact asymptotics for the completion time and the communication complexity for large network size which reveal the effect of the hop limit count. Perhaps surprisingly, we find that both flooding algorithms perform near optimum and that the simpler (lazy) algorithm is only slightly worse than the other, more complicated algorithm. The results provide insights into performance of networked systems that use hop limits, for example, in the contexts of peer-to-peer systems and mobile ad-hoc networks.

A note on efficient aggregate queries in sensor networks

Abstract: We consider a scenario where nodes in a sensor network hold numeric items, and the task is to evaluate simple functions of the distributed data. In this note we present distributed protocols for computing the median with sublinear space and communication complexity per node. Specifically, we give a deterministic protocol for computing median with polylog complexity and a randomized protocol that computes an approximate median with polyloglog communication complexity per node. On the negative side, we observe that any deterministic protocol that counts the number of distinct data items must have linear complexity in the worst case.

Design and Evaluation of Network Topology-/Speed- Aware Broadcast Algorithms for InfiniBand Clusters

Abstract: It is an established fact that the network topology can have an impact on the performance of scientific parallel applications. However, little work has been done to design an easy to use solution inside a communication library supporting a parallel programming model where the complexities of making the application performance network topology agnostic is hidden from the end user. Similarly, the rapid improvements in networking technology and speed are resulting in many commodity clusters becoming heterogeneous, with respect to networking speed. For example, switches and adapters belonging to different generations (SDR - 8 Gbps, DDR - 16 Gbps and QDR - 36 Gbps speeds in InfiniBand) are integrated into a single system. This leads to an additional challenge to make the communication library aware of the performance implications of heterogeneous link speeds. Accordingly, the communication library can perform optimizations taking link speed into account. In this paper, we propose a framework to automatically detect the topology and speed of an InfiniBand network and make it available to users through an easy to use interface. We also make design changes inside the MPI library to dynamically query this topology detection service and to form a topology model of the underlying network. We have redesigned the broadcast algorithm to take into account this network topology information and dynamically adapt the communication pattern to best fit the characteristics of the underlying network. To the best of our knowledge, this is the first such work for InfiniBand clusters. Our experimental results show that, for large homogeneous systems and large message sizes, we get up to 14% improvement in the latency of the broadcast operation using our proposed network topology-aware scheme over the default scheme at the micro-benchmark level. At the application level, the proposed framework delivers up to 8% improvement in total application run-time especially as job size scales up. The proposed network speed-aware algorithms are able to attain micro-benchmark performance on the heterogeneous SDR-DDR InfiniBand cluster to perform on par with runs on the DDR only portion of the cluster for small to medium sized messages. We also demonstrate that the network speed aware algorithms perform 70% to 100% better than the naive algorithms when both are run on the heterogeneous SDR-DDR InfiniBand cluster.