Sorted Range Reporting Revisited

Sorted Range Reporting

We consider a variant of the orthogonal range reporting problem when all points should be reported in the sorted order of their x-coordinates. We show that reporting two-dimensional points with this additional condition can be organized (almost) as efficiently as the standard range reporting. Moreover, our results generalize and improve the previously known results for the orthogonal range succ...

Online Sorted Range Reporting

We study the following one-dimensional range reporting problem: On an array A of n elements, support queries that given two indices i ≤ j and an integer k report the k smallest elements in the subarray A[i..j] in sorted order. We present a data structure in the RAM model supporting such queries in optimal O(k) time. The structure uses O(n) words of space and can be constructed in O(n log n) tim...

Order-sorted Equational Unification Revisited

This paper presents a rule-based algorithm for performing order-sorted E-unification using an unsorted E-unification decision procedure under assumptions about E that are commonly satisfied in practice. We have implemented this algorithm in Maude for use with the Maude-NRL protocol analyzer and have used CiME for unsorted E-unification for E any set of AC and ACU axioms. In many examples of int...

Run Generation Revisited: What Goes Up May or May Not Come Down

We revisit the classic problem of run generation. Run generation is the first phase of external-memory sorting, where the objective is to scan through the data, reorder elements using a small buffer of size M , and output runs (contiguously sorted chunks of elements) that are as long as possible. We develop algorithms for minimizing the total number of runs (or equivalently, maximizing the aver...

Through the Looking Glass revisited: the need for more meaning and less drama in the reporting of dose and dose reduction in CT.