Communication complexity

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

A trade-off between information and communication in broadcast protocols

Abstract: This paper concerns the message complexity of broadcast in arbitrary point-to-point communication networks. Broadcast is a task initiated by a single processor that wishes to convey a message to all processors in the network. The widely accepted model of communication networks, in which each processor initially knows the identity of its neighbors but does not know the entire network topology, is assumed. Although it seems obvious that the number of messages required for broadcast in this model equals the number of links, no proof of this basic fact has been given before.It is shown that the message complexity of broadcast depends on the exact complexity measure. If messages of unbounded length are counted at unit cost, then broadcast requires T(uVu) messages, where V is the set of processors in the network. It is proved that, if one counts messages of bounded length, then broadcast requires T(uEu) messages, where E is the set of edges in the network.Assuming an intermediate model in which each vertex knows the topology of the network in radius r ≥ 1 from itself, matching upper and lower bounds of T(min{uEu, uVu1+T(l)/r}) is proved on the number of messages of bounded length required for broadcast. Both the upper and lower bounds hold for both synchronous and asynchronous network models.The same results hold for the construction of spanning trees, and various other global tasks.

Interconnect-Aware Coherence Protocols for Chip Multiprocessors

Abstract: Improvements in semiconductor technology have made it possible to include multiple processor cores on a single die. Chip Multi-Processors (CMP) are an attractive choice for future billion transistor architectures due to their low design complexity, high clock frequency, and high throughput. In a typical CMP architecture, the L2 cache is shared by multiple cores and data coherence is maintained among private L1s. Coherence operations entail frequent communication over global on-chip wires. In future technologies, communication between different L1s will have a significant impact on overall processor performance and power consumption. On-chip wires can be designed to have different latency, bandwidth, and energy properties. Likewise, coherence protocol messages have different latency and bandwidth needs. We propose an interconnect composed of wires with varying latency, bandwidth, and energy characteristics, and advocate intelligently mapping coherence operations to the appropriate wires. In this paper, we present a comprehensive list of techniques that allow coherence protocols to exploit a heterogeneous interconnect and evaluate a subset of these techniques to show their performance and power-efficiency potential. Most of the proposed techniques can be implemented with a minimum complexity overhead.

Lower Bounds in Communication Complexity

Abstract: In the 30 years since its inception, communication complexity has become a vital area of theoretical computer science. The applicability of communication complexity to other areas, including circuit and formula complexity, VLSI design, proof complexity, and streaming algorithms, has meant that it has attracted a lot of interest. Lower Bounds in Communication Complexity focuses on showing lower bounds on the communication complexity of explicit functions. It treats different variants of communication complexity, including randomized, quantum, and multiparty models. Many tools have been developed for this purpose from a diverse set of fields including linear algebra, Fourier analysis, and information theory. As is often the case in complexity theory, demonstrating a lower bound is usually the more difficult task. Lower Bounds in Communication Complexity describes a three-step approach for the development and application of these techniques. This approach can be applied in much the same way for different models, be they randomized, quantum, or multiparty. Lower Bounds in Communication Complexity is an ideal primer for anyone with an interest in this current and popular topic.

Efficient Privacy-Preserving k-Nearest Neighbor Search

Abstract: We give efficient protocols for secure and private k-nearest neighbor (k-NN) search, when the data is distributed between two parties who want to cooperatively compute the answers without revealing to each other their private data. Our protocol for the single-step k-NN search is provably secure and has linear computation and communication complexity. Previous work on this problem had a quadratic complexity, and also leaked information about the parties' inputs. We adapt our techniquesto also solve the general multi-step k-NN search, and describe a specific embodiment of it for the case of sequence data. The protocols and correctness proofs can be extended to suit other privacy-preserving data mining tasks, such as classification and outlier detection.

Cryptographic primitives enforcing communication and storage complexity

Abstract: We introduce a new type of cryptographic primitives which enforce high communication or storage complexity. To evaluate these primitives on a random input, one has to engage in a protocol of high communication complexity, or one has to use a lot of storage. Therefore, the ability to compute these primitives constitutes a certain "proof of work," since the computing party is forced to contribute a lot of its communication or storage resources to this task. Such primitives can be used in applications which deal with nonmalicious but selfishly resource-maximizing parties. For example, they can be useful in constructing peer-to-peer systems which are robust against so called "free riders." In this paper we define two such primitives, a communication-enforcing signature and a storage-enforcing commitment scheme, and we give constructions for both.