In the Order-Maintenance Problem, the objective is to maintain a total order subject to insertions, deletions, and precedence queries. Known optimal solutions, due to Dietz and Sleator, are complicated. We present new algorithms that match the bounds of Dietz and Sleator. Our solutions are simple, and we present experimental evidence that suggests that they are superior in practice.

Abstract not found

The rank aggregation problem is to combine many different rank orderings on the same set of candidates, or alternatives, in order to obtain a "better" ordering. Rank aggregation has been studied extensively in the context of social choice theory, where several "voting paradoxes" have been discovered.

We give an O(n √ lg n)-time algorithm for counting the number of inversions in a permutation on n elements. This improves a long-standing previous bound of O(n lg n / lg lg n) that followed from Dietz’s data structure [WADS’89], and answers a question of Andersson and Petersson [SODA’95]. As Dietz’s result is known to be optimal for the related dynamic rank problem, our result demonstrates a significant improvement in the offline setting. Our new technique is quite simple: we perform a “vertical partitioning ” of a trie (akin to van Emde Boas trees), and use ideas from external memory. However, the technique finds numerous applications: for example, we obtain • in d dimensions, an algorithm to answer n offline orthogonal range counting queries in time O(n lg d−2+1/d n); • an improved construction time for online data structures for orthogonal range counting; • an improved update time for the partial sums problem; • faster Word RAM algorithms for finding the maximum depth in an arrangement of axis-aligned rectangles, and for the slope selection problem. As a bonus, we also give a simple (1 + ε)-approximation algorithm for counting inversions that runs in linear time, improving the previous O(n lg lg n) bound by Andersson and Petersson.

A key capability of data-race detectors is to determine whether one thread executes logically in parallel with another or whether the threads must operate in series. This paper provides two algorithms, one serial and one parallel, to maintain series-parallel (SP) relationships “on the fly” for fork-join multithreaded programs. The serial SP-order algorithm runs in O(1) amortized time per operation. In contrast, the previously best algorithm requires a time per operation that is proportional to Tarjan’s functional inverse of Ackermann’s function. SP-order employs an order-maintenance data structure that allows us to implement a more efficient “English-Hebrew ” labeling scheme than was used in earlier race detectors, which immediately yields an improved determinacy-race detector. In particular, any fork-join program running in T1 time on a single processor can be checked on the fly for determinacy races in

We describe a load-balancing mechanism for assigning elements to servers in a distributed data structure that supports range queries. The mechanism ensures both load-balancing with respect to an arbitrary load measure specified by the user and geographical locality, assigning elements with similar keys to the same server. Though our mechanism is specifically designed to improve the performance of skip graphs, it can be adapted to provide deterministic, locality-preserving load-balancing to any distributed data structure that orders machines in a ring or line.

Deciding which kind of visiting strategy accumulates high-quality pages more quickly is one of the most often debated issues in the design of web crawlers. This paper proposes a related, and previously overlooked, measure of effectivity for crawl strategies: whether the graph obtained after a partial visit is in some sense representative of the underlying web graph as far as the computation of PageRank is concerned. More precisely, we are interested in determining how rapidly the computation of PageRank over the visited subgraph yields rankings that agree with the ones computed in the complete graph; ranks are compared using Kendall’s τ. We describe a number of large-scale experiments that show the following paradoxical effect: visits that gather PageRank more quickly (e.g., highest-quality first) are also those that tend to miscalculate PageRank. Finally, we perform the same kind of experimental analysis on some synthetic random graphs, generated using well-known web-graph models: the results are almost opposite to those obtained on real web graphs. 1

Abstract not found

Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy.