No abstract

We introduce a novel approach for sending messages over lossy packet-based networks. The new method, called Priority Encoding Transmission, allows a user to specify a different priority on each segment of the message. Based on the priorities, the sender uses the system to encode the segments into packets for transmission. The system ensures recovery of the segments in order of their priority. The priority of a segment determines the minimum number of packets sufficient to recover the segment.We define a measure for a set of priorities, called the rate, which dictates how much information about the message must be contained in each bit of the encoding. We develop systems for implementing any set of priorities with rate equal to one. We also give an information-theoretic proof that there is no system that implements a set of priorities with rate greater than one. This work has applications to multi-media and high speed networks applications, especially in those with bursty sources and multiple receivers with heterogeneous capabilities.

No abstract

Papadimitriou introduced several classes of NP search problems based on combinatorial principles which guarantee the existence of solutions to the problems. Many interesting search problems not known to be solvable in polynomial time are contained in these classes, and a number of them are complete problems. We consider the question of the relative complexity of these search problem classes. We prove several separations which show that in a generic relativized world, the search classes are distinct and there is a standard search problem in each of them that is not computationally equivalent to any decision problem. (Naturally, absolute separations would imply that P 6 = NP.) Our separation proofs have interesting combinatorial content and go to the heart of the combinatorial principles on which the classes are based. We derive one result via new lower bounds on the degrees of polynomials asserted to exist by Hilbert's Nullstellensatz over nite elds.

We give a scalable ((1+ǫ)-speed O(1)-competitive) nonclairvoyant algorithm for scheduling jobs with sublinear nondecreasing speed-up curves on multiple processors with the objective of average response time.