1,071 research outputs found
Insertion Sort is O(n log n)
Traditional Insertion Sort runs in O(n^2) time because each insertion takes
O(n) time. When people run Insertion Sort in the physical world, they leave
gaps between items to accelerate insertions. Gaps help in computers as well.
This paper shows that Gapped Insertion Sort has insertion times of O(log n)
with high probability, yielding a total running time of O(n log n) with high
probability.Comment: 6 pages, Latex. In Proceedings of the Third International Conference
on Fun With Algorithms, FUN 200
Reallocation Problems in Scheduling
In traditional on-line problems, such as scheduling, requests arrive over
time, demanding available resources. As each request arrives, some resources
may have to be irrevocably committed to servicing that request. In many
situations, however, it may be possible or even necessary to reallocate
previously allocated resources in order to satisfy a new request. This
reallocation has a cost. This paper shows how to service the requests while
minimizing the reallocation cost. We focus on the classic problem of scheduling
jobs on a multiprocessor system. Each unit-size job has a time window in which
it can be executed. Jobs are dynamically added and removed from the system. We
provide an algorithm that maintains a valid schedule, as long as a sufficiently
feasible schedule exists. The algorithm reschedules only a total number of
O(min{log^* n, log^* Delta}) jobs for each job that is inserted or deleted from
the system, where n is the number of active jobs and Delta is the size of the
largest window.Comment: 9 oages, 1 table; extended abstract version to appear in SPAA 201
Cache-Oblivious Persistence
Partial persistence is a general transformation that takes a data structure
and allows queries to be executed on any past state of the structure. The
cache-oblivious model is the leading model of a modern multi-level memory
hierarchy.We present the first general transformation for making
cache-oblivious model data structures partially persistent
An in situ evaluation of nutrient effects in lakes
A method for performing in situ nutrient enrichment experiments on natural likeJ)liytoplankton ccmmunities was developed and evaluated. One set of experiments in which it was employed was designed to detect limiting nutrients and to provide a basis for predicting future experiment results. Productivity increased in response to all three of the treatment variables used, N, P, and EDTA, but response patterns varied from experiment to experiment. Individual species responded differently to different treatments, and interactions among the treatment variables were important in shaping the community responses to mixtures of two or three variables. The most consistent features of the productivity results were incorporated into a most probable response pattern, which was partially validated by a second series of experiments
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