The space-optimal version of a known rectangle enclosure reporting algorithm

Bozanis, Panayiotis; Kitsios, Nectarios; Makris, Christos; Tsakalidis, Athanasios K.

doi:10.1016/s0020-0190(96)00186-x

Cited by 8 publications

(8 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Gupta et al [4] reported an algorithm with linear space requirement based on the 4-D dominance reporting method. Improvements of this algorithm are found in Bozanis et al [3] and Lagogiannis et al [5].…”

Section: Prior Workmentioning

confidence: 98%

Algorithm for the Removal of Rectangle Containment for Rectangle Spline Generation

Piegl

Kulkarni

Rajab

2014

Computer-Aided Design and Applications

View full text Add to dashboard Cite

Section: Prior Workmentioning

confidence: 98%

Algorithm for the Removal of Rectangle Containment for Rectangle Spline Generation

Piegl

Kulkarni

Rajab

2014

Computer-Aided Design and Applications

View full text Add to dashboard Cite

“…The term O(log B n), on the other hand, is also compulsory due to a reduction from predecessor search. First, it is well-known (see, e.g., [8]…”

Section: Constructing the Ppb-treementioning

confidence: 99%

“…• CatenateAndAttrite(Q1, Q2) 8 We define the ordering of the elements in a record r to be all elements of its buffer l followed by all elements in the I/O-CPQA referenced by pointer p. We define the queue order of I/O-CPQA Q to be F (Q), C(Q), B(Q) and D1(Q), . .…”

Section: I/o-efficient Catenable Attrition Priority Queuesmentioning

confidence: 99%

I/O-efficient planar range skyline and attrition priority queues

Kejlberg-Rasmussen

Tao

Tsakalidis

et al. 2013

Proceedings of the 32nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

View full text Add to dashboard Cite

We study the static and dynamic planar range skyline reporting problem in the external memory model with block size B, under a linear space budget. The problem asks for an O(n/B) space data structure that stores n points in the plane, and supports reporting the k maximal input points (a.k.a. skyline) among the points that lie within a givenone of its edges is grounded, two variants arise: topopen for β2 = ∞ and left-open for α1 = −∞ (symmetrically bottom-open and right-open) queries.We present optimal static data structures for top-open queries, for the cases where the universe is R 2 , a U × U grid, and rank space [O(n)] 2 . We also show that left-open queries are harder, as they require Ω((n/B) + k/B) I/Os for > 0, when only linear space is allowed. We show that the lower bound is tight, by a structure that supports 4-sided queries in matching complexities. Interestingly, these lower and upper bounds coincide with those of the planar orthogonal range reporting problem, i.e., the skyline requirement does not alter the problem difficulty at all! Finally, we present the first dynamic linear space data structure that supports top-open queries in O(log 2B n + k/B 1− ) and updates in O(log 2B n) worst case I/Os, for ∈ [0, 1]. This also yields a linear space data structure for 4-sided queries with optimal query I/Os and O(log(n/B)) amortized update I/Os. We consider of independent interest the main component of our dynamic structures, a new realtime I/O-efficient and catenable variant of the fundamental structure priority queue with attrition by Sundar. * The full version is found on http://arxiv.org under the same title.

show abstract

“…Όλοι οι αλγόριθμοι που θα παρουσιάσουμε στη συνέχεια της εργασίας έχουν δημοσιευθεί από τον συγγραφέα σε συνέδρια-περιοδικά ή έχουν υποβληθεί τζρος δημοσίευση. Το κεφάλαιο 2 βασίζεται στην εργασία [22], το κεφάλαιο 3 στις εργασίες [25,26,100,101], το κεφάλαιο 4 στην εργασία [102], το κεφάλαιο 5 στις εργασίες [23,24,26] και το κεφάλαιο 6 στην εργασία [99].…”

Section: παρατήρησηunclassified

Βασικες Δομες Δεδομενων Και Η Εφαρμογη Τους Στην Υπολογιστικη Γεωμετρια Και Στην Ανακτηση Πληροφοριας

Μακρησ¹

View full text Add to dashboard Cite

The space-optimal version of a known rectangle enclosure reporting algorithm

Cited by 8 publications

References 9 publications

Algorithm for the Removal of Rectangle Containment for Rectangle Spline Generation

Algorithm for the Removal of Rectangle Containment for Rectangle Spline Generation

I/O-efficient planar range skyline and attrition priority queues

Βασικες Δομες Δεδομενων Και Η Εφαρμογη Τους Στην Υπολογιστικη Γεωμετρια Και Στην Ανακτηση Πληροφοριας

Contact Info

Product

Resources

About