Dynamic Trees with Almost-Optimal Access Cost

An optimal binary search tree for an access sequence on elements is a static tree that minimizes the total search cost. Constructing perfectly optimal binary search trees is expensive so the most efficient algorithms construct almost optimal search trees. There exists a long literature of constructing almost optimal search trees dynamically, i.e., when the access pattern is not known in advance. All of these trees, e.g., splay trees and treaps, provide a multiplicative approximation to the optimal search cost. In this paper we show how to maintain an almost optimal weighted binary search tree under access operations and insertions of new elements where the approximation is an additive constant. More technically, we maintain a tree in which the depth of the leaf holding an element e_i does not exceed min(log(W/w_i),log n)+O(1) where w_i is the number of times e_i was accessed and W is the total length of the access sequence. Our techniques can also be used to encode a sequence of m symbols with a dynamic alphabetic code in O(m) time so that the encoding length is bounded by m(H+O(1)), where H is the entropy of the sequence. This is the first efficient algorithm for adaptive alphabetic coding that runs in constant time per symbol

Crowdsourced Live Streaming over the Cloud

Empowered by today's rich tools for media generation and distribution, and the convenient Internet access, crowdsourced streaming generalizes the single-source streaming paradigm by including massive contributors for a video channel. It calls a joint optimization along the path from crowdsourcers, through streaming servers, to the end-users to minimize the overall latency. The dynamics of the video sources, together with the globalized request demands and the high computation demand from each sourcer, make crowdsourced live streaming challenging even with powerful support from modern cloud computing. In this paper, we present a generic framework that facilitates a cost-effective cloud service for crowdsourced live streaming. Through adaptively leasing, the cloud servers can be provisioned in a fine granularity to accommodate geo-distributed video crowdsourcers. We present an optimal solution to deal with service migration among cloud instances of diverse lease prices. It also addresses the location impact to the streaming quality. To understand the performance of the proposed strategies in the realworld, we have built a prototype system running over the planetlab and the Amazon/Microsoft Cloud. Our extensive experiments demonstrate that the effectiveness of our solution in terms of deployment cost and streaming quality

In pursuit of the dynamic optimality conjecture

In 1985, Sleator and Tarjan introduced the splay tree, a self-adjusting binary search tree algorithm. Splay trees were conjectured to perform within a constant factor as any offline rotation-based search tree algorithm on every sufficiently long sequence---any binary search tree algorithm that has this property is said to be dynamically optimal. However, currently neither splay trees nor any other tree algorithm is known to be dynamically optimal. Here we survey the progress that has been made in the almost thirty years since the conjecture was first formulated, and present a binary search tree algorithm that is dynamically optimal if any binary search tree algorithm is dynamically optimal.Comment: Preliminary version of paper to appear in the Conference on Space Efficient Data Structures, Streams and Algorithms to be held in August 2013 in honor of Ian Munro's 66th birthda