Showing papers by "Richard Cole published in 2006"

Searching dynamic point sets in spaces with bounded doubling dimension

Abstract: We present a new data structure that facilitates approximate nearest neighbor searches on a dynamic set of points in a metric space that has a bounded doubling dimension. Our data structure has linear size and supports insertions and deletions in O(log n) time, and finds a (1+e)-approximate nearest neighbor in time O(log n) + (1/e)O(1). The search and update times hide multiplicative factors that depend on the doubling dimension; the space does not. These performance times are independent of the aspect ratio (or spread) of the points.

Bottleneck links, variable demand, and the tragedy of the commons

Abstract: The price of anarchy, a measure of the inefficiency of selfish behavior, has been successfully analyzed in a diverse array of models over the past five years. The overwhelming majority of this work has studied optimization problems that sought an optimal way to allocate a fixed demand to resources whose performance degrades with increasing congestion. While fundamental, such problems overlook a crucial feature of many applications: the intrinsic coupling of the quality or cost of a resource and the demand for that resource. This coupling motivates allowing demand to vary with congestion, which in turn can lead to "the tragedy of the commons"---severe inefficiency caused by the overconsumption of a shared resource.Allowing the demand for resources to vary with their congestion illuminates a second issue with existing studies of the price of anarchy: the standard additive method of aggregating the costs of different resources in a player's strategy is inappropriate for some important applications, including many of those with variable demand. For example, in networking applications a key performance metric is the achievable throughput along a path, which is controlled by its bottleneck (most congested) edge. This disconnect motivates consideration of nonlinear cost aggregation functions, such as the lp norms.In this paper, we initiate the study of the price of anarchy with variable demand and with broad classes of nonlinear aggregation functions. We focus on selfish routing in single- and multicommodity networks, and on the lp norms for 1 ≤ p ≤ ∞; our main results are as follows.• For a natural "prize-collecting" objective function, the price of anarchy in multicommodity networks with variable demand is no larger than that in fixed-demand networks. Thus the inefficiency arising from the tragedy of the commons is no more severe than that from routing inefficiencies.• Using the lp norm with 1

Suffix trays and suffix trists: structures for faster text indexing

Abstract: Suffix trees and suffix arrays are two of the most widely used data structures for text indexing. Each uses linear space and can be constructed in linear time [3,5,6,7]. However, when it comes to answering queries, the prior does so in O(mlog|Σ|) time, where m is the query size, |Σ| is the alphabet size, and the latter does so in O(m+logn), where n is the text size. We propose a novel way of combining the two into, what we call, a suffix tray. The space and construction time remain linear and the query time improves to O(m+log|Σ|). We also consider the online version of indexing, where the indexing structure continues to update the text online and queries are answered in tandem. Here we suggest a suffix trist, a cross between a suffix tree and a suffix list. It supports queries in O(m+log|Σ|). The space and text update time of a suffix trist are the same as for the suffix tree or the suffix list.

Suffix Trays and Suffix Trists : Structures for Faster Text Indexing

Abstract: Suffix trees and suffix arrays are two of the most widely used data structures for text indexing. Each uses linear space and can be constructed in linear time [3,5,6,7]. However, when it comes to answering queries, the prior does so in O(m log |Σ|) time, where m is the query size, |Σ| is the alphabet size, and the latter does so in 0(m + log n), where n is the text size. We propose a novel way of combining the two into, what we call, a suffix tray. The space and construction time remain linear and the query time improves to 0(m + log |Σ|). We also consider the online version of indexing, where the indexing structure continues to update the text online and queries are answered in tandem. Here we suggest a suffix trist, a cross between a suffix tree and a suffix list. It supports queries in 0(m,+log |Σ|). The space and text update time of a suffix trist are the same as for the suffix tree or the suffix list.