We study the communication complexity of the set disjointness problem in the general multi-party model. For t players, each holding a subset of a universe of size n, we establish a near-optimal lower bound of Ω(n/(t log t)) on the communication complexity of the problem of determining whether their sets are disjoint. In the more restrictive one-way communication model, in which the players are required to speak in a predetermined order, we improve our bound to an optimal Ω(n/t). These results improve upon the earlier bounds of Ω(n/t 2 ) in the general model, and Ω(ε 2 n/t 1+ε ) in the one-way model, due to Jayram, Kumar, and Sivakumar [5]. As in the case of earlier results, our bounds apply to the unique intersection promise problem. This communication problem is known to have connections with the space complexity of approximating frequency moments in the data stream model.Our results lead to an improved space complexity lower bound of Ω(n 1−2/k / log n) for approximating the k th frequency moment with a constant number of passes over the input, and a technical improvement to Ω(n 1−2/k ) if only one pass over the input is permitted.Our proofs rely on the information theoretic direct sum decomposition paradigm of . Our improvements stem from novel analytical tech- *

Abstract-Distance estimation is important to many Internet applications. It can aid a WWW client when selecting among several potential candidate servers, or among candidate peer-to-peer servers. It can also aid in building efficient overlay or peer-to-peer networks that dynamically react to change in the underlying Internet. One of the approaches to distance (i.e., time delay) estimation in the Internet is based on placing Tracer stations in key locations and conducting measurements between them. The Tracers construct an approximated map of the Internet after processing the information obtained from these measurements.This work presents a novel algorithm, based on Algebraic tools, that computes additional distances, which are not explicitly measured. As such, the algorithm extracts more information from the same amount of measurement data.Our algorithm has several practical impacts. First, it can reduce the number of Tracers and measurements without sacrificing information. Second, our algorithm is able to compute distance estimates between locations where Tracers cannot be placed.To evaluate the algorithm's performance, we tested it both on randomly generated topologies and on real Internet measurements. Our results show that the algorithm computes up to 50-200% additional distances beyond the basic Tracer-to-Tracer measurements.

We prove the first time-space lower bound trade-offs for randomized computation of decision problems. The bounds hold even in the case that the computation is allowed to have arbitrary probability of error on a small fraction of inputs. Our techniques are extension of those used by Ajtai and by Beame, Jayram, and Saks that applied to deterministic branching programs. Our results also give a quantitative improvement over the previous results.Previous time-space trade-off results for decision problems can be divided naturally into results for functions with Boolean domain, that is, each input variable is {0, 1}-valued, and the case of large domain, where each input variable takes on values from a set whose size grows with the number of variables.In the case of Boolean domain, Ajtai exhibited an explicit class of functions, and proved that any deterministic Boolean branching program or RAM using space S = o(n) requires superlinear time T to compute them. The functional form of the superlinear bound is not given in his paper, but optimizing the parameters in his arguments gives T = (n log log n/ log log log n) for S = O(n 1− ). 155For the same functions considered by Ajtai, we prove a time-space trade-off (for randomized branching programs with error) of the form T = (n √ log(n/S)/ log log(n/S)). In particular, for space O(n 1− ), this improves the lower bound on time to (n √ log n/ log log n). In the large domain case, we prove lower bounds of the form T = (n √ log(n/S)/ log log(n/S)) for randomized computation of the element distinctness function and lower bounds of the form T = (n log(n/S)) for randomized computation of Ajtai's Hamming closeness problem and of certain functions associated with quadratic forms over large fields.

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Cutting fluid is traditionally used to remove heat generated during the cutting process, but it can cause environmental pollution, health hazards, and high cost of production. Dry cutting, without using the cooling liquid, is thus desirable and promising for the machining industry to produce components and products, both ecologically and more economically. In this paper, an internally cooled cutting tool for dry cutting is presented as a temperature-sensored smart cutting tool in its own right, with further applications for adaptive machining purposes. The cutting tool is characterized by a simple changeable internal cooling structure near the cutting tip. Simulations were performed to study the theoretical cooling efficiency and to optimize the cooling structure by combining it with the Taguchi Method. Furthermore, cutting trials were carried out to validate the novel cutting tool experimentally.