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Fractional cascading: I. A data structuring technique

Bernard Chazelle, Leonidas J. Guibas
1986 Algorithmica  
Without expanding the storage by more than a constant factor, we can build a data-structure, called a fractional cascading structure, in which all original searches after the first can be carried out at  ...  Several results related to the dynamization of this structure are also presented. A companion paper gives numerous applications of this technique to geometric problems.  ...  We are also grateful to Marc Brown for programming a preliminary version of fractional cascading in the static case. The idea for the construction in the following appendix is due to Jorge Stolfi.  ... 
doi:10.1007/bf01840440 fatcat:k3qxz2xnerg5lnoq22opujipsu

Dynamic fractional cascading

Kurt Mehlhorn, Stefan Näher
1990 Algorithmica  
Chazelle and Gu ibas recently introduced fractional cascading ... a general techn ique for solving this type of problem.  ...  In the present paper we show that fractional cascading also supports insertions into and deletions from the lists efficiently.  ...  in order to link the fractional cascading structure with the data ,tructure defined above.  ... 
doi:10.1007/bf01840386 fatcat:esxnk4ygpff6xngrsmblc6xova

A Lower Bound for Dynamic Fractional Cascading [article]

Peyman Afshani
2020 arXiv   pre-print
We investigate the limits of one of the fundamental ideas in data structures: fractional cascading.  ...  We prove a lower bound of Ω( log n √(loglog n)) on the worst-case query time of dynamic fractional cascading, when queries are paths of length O(log n).  ...  By now fractional cascading is one of the fundamental and classical techniques in data structures and in fact, it is routinely taught in various advanced data structures courses around the world.  ... 
arXiv:2011.00503v2 fatcat:hj5rsxxutzc25jmdrg6ospvk2m

2D Fractional Cascading on Axis-aligned Planar Subdivisions [article]

Peyman Afshani, Pingan Cheng
2020 arXiv   pre-print
Fractional cascading is one of the influential techniques in data structures, as it provides a general framework for solving the important iterative search problem.  ...  fractional cascading is fundamentally a 1D technique.  ...  In recent years, interestingly, a technique similar to 2D fractional cascading has been used to improve many classical computational geometry data structures.  ... 
arXiv:2009.05541v2 fatcat:4fzeakxnuzebdmyf3npxg3iwfa

Parallel fractional cascading on hypercube multiprocessors

Frank Dehne, Afonso Ferreira, Andrew Rau-Chaplin
1992 Computational geometry  
., A. Ferreira and A. Rau-Chaplin, Parallel fractional cascading on hypercube multiprocessors, Computational Geometry: Theory and Applications 2 (1992) 141-167. F. Dehne et al. the same time.  ...  We present two parallel computational geometry applications of this technique: multiple stabbing of a simple polygonal path and multiple slanted range search.  ...  Problem overview Fractional cascading, as described by Chazelle and Guibas [7], is a general data structuring technique in which catalog graphs are used to represent data structures.  ... 
doi:10.1016/0925-7721(92)90005-d fatcat:525emsbofrg4zbnkqxnwca45za

An implementation of range trees with fractional cascading in C++ [article]

Vissarion Fisikopoulos
2011 arXiv   pre-print
We also document our implementation of range trees with fractional cascading in C++ using STL and generic programming techniques.  ...  In this technical report we study the implementation issues of range trees with fractional cascading, named layered range trees.  ...  Acknowledgements This project started as a course project in the graduate course of Computational Geometry, National and Kapodistrian University of Athens 2008-2009 under the supervision of professor Ioannis  ... 
arXiv:1103.4521v1 fatcat:syghxla5engy3pdwwt4za4wq6i

Optimal Cooperative Search in Fractional Cascaded Data Structures

R. Tamassia, J.S. Vitter
1996 Algorithmica  
Fractional cascading is a technique designed to allow e cient sequential search i n a graph with catalogs of total size n. The search consists of locating a key in the catalogs along a path.  ...  In this paper we show h o w to preprocess a variety of fractional cascaded data structures whose underlying graph is a tree so that searching can be done e ciently in parallel.  ...  The search described above in the fractional cascaded data structure is sequential in nature.  ... 
doi:10.1007/s004539900009 fatcat:jllrdwn23zfkzomgy23jkb6jpi

Cascade optical chromatography for sample fractionation

Alex Terray, Joseph D. Taylor, Sean J. Hart
2009 Biomicrofluidics  
We demonstrate this technique coupled with an advanced microfluidic platform and show how it can be used as an effective method to fractionate particles from an injected multicomponent sample.  ...  Our advanced three-stage microfluidic design accommodates three lasers simultaneously to effectively create a sequential cascade optical chromatographic separation system.  ...  Lisa A. Fitzgerald ͑NRC Postdoctoral Fellow at the Naval Research Laboratory͒ for supplying the E. coli samples.  ... 
doi:10.1063/1.3262415 pmid:20216968 pmcid:PMC2835286 fatcat:zi44zsjmcbhh3e2cj2o4qaswui

Optimal cooperative search in fractional cascaded data structures

T. Tamassia, J. S. Vitter
1990 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures - SPAA '90  
Fractional cascading is a technique designed to allow e cient sequential search i n a graph with catalogs of total size n. The search consists of locating a key in the catalogs along a path.  ...  In this paper we show h o w to preprocess a variety of fractional cascaded data structures whose underlying graph is a tree so that searching can be done e ciently in parallel.  ...  The search described above in the fractional cascaded data structure is sequential in nature.  ... 
doi:10.1145/97444.97698 dblp:conf/spaa/TamassiaV90 fatcat:54jnzrvw7fbnllc6gtircupbra

Optimal cooperative search in fractional cascaded data structures

R. Tamassia, J. S. Vitter
1996 Algorithmica  
Fractional cascading is a technique designed to allow e cient sequential search i n a graph with catalogs of total size n. The search consists of locating a key in the catalogs along a path.  ...  In this paper we show h o w to preprocess a variety of fractional cascaded data structures whose underlying graph is a tree so that searching can be done e ciently in parallel.  ...  The search described above in the fractional cascaded data structure is sequential in nature.  ... 
doi:10.1007/bf01941686 fatcat:zjd3vb3h65gfxdebf6ferhz3ty

Fractionally cascaded information in a sensor network

Jie Gao, Leonidas J. Guibas, John Hershberger, Li Zhang
2004 Proceedings of the third international symposium on Information processing in sensor networks - IPSN'04  
We study in particular how this principle of fractionally cascaded information can be exploited to answer range queries about the sampled field efficiently.  ...  The principle we propose is that a sensor should know a "fraction" of the information from distant parts of the network, in an exponentially decaying fashion by distance.  ...  Research by Jie Gao and Leonidas Guibas was supported by the NSF grant CCR-0204486, the DARPA Sensor Information Technology Program under contract F30602-00-C-0139, ONR MURI grant N00014-02-1-0720, and a  ... 
doi:10.1145/984622.984668 dblp:conf/ipsn/GaoGHZ04 fatcat:yoeaa5qwlbdq7fcukteqmn4aj4

Hopcroft's Problem, Log-Star Shaving, 2D Fractional Cascading, and Decision Trees [article]

Timothy M. Chan, Da Wei Zheng
2021 arXiv   pre-print
We describe two interesting and different ways to achieve the result: the first is randomized and uses a new 2D version of fractional cascading for arrangements of lines; the second is deterministic and  ...  uses decision trees in a manner inspired by the sorting technique of Fredman (1976).  ...  Our approach via 2D fractional cascading, in combination with Fredman's decision tree technique, also leads to new randomized data structures for 2D halfplane range counting, for example, achieving P (  ... 
arXiv:2111.03744v1 fatcat:3emz4diddvgupbqzvs3ez6cr2e

Design of Cascaded and Shifted Fractional-Order Lead Compensators for Plants with Monotonically Increasing Lags

Guido Maione
2020 Fractal and Fractional  
This paper concerns cascaded, shifted, fractional-order, lead compensators made by the serial connection of two stages introducing their respective phase leads in shifted adjacent frequency ranges.  ...  Adding up leads in these intervals gives a flat phase in a wide frequency range. Moreover, the simple elements of the cascade can be easily realized by rational transfer functions.  ...  Some other authors proposed curve fitting techniques (with built-in Matlab functions) that use frequency response data of fractional-order operators to improve the ORA, the modified ORA, or the Matsuda  ... 
doi:10.3390/fractalfract4030037 fatcat:fbryo6pn3ngudonegmla2zau24

Discrepancy-Sensitive Dynamic Fractional Cascading, Dominated Maxima Searching, and 2-d Nearest Neighbors in Any Minkowski Metric [article]

Mikhail J. Atallah, Marina Blanton, Michael T. Goodrich, Stanislas Polu
2009 arXiv   pre-print
This paper studies a discrepancy-sensitive approach to dynamic fractional cascading.  ...  We provide an efficient data structure for dominated maxima searching in a dynamic set of points in the plane, which in turn leads to an efficient dynamic data structure that can answer queries for nearest  ...  Thus, achieving a dynamic data fractional cascading data structure has an increased complexity.  ... 
arXiv:0904.4670v1 fatcat:nbm36og7sfhp7a6hmfv7kp4zuy

Lower bounds for intersection searching and fractional cascading in higher dimension

Bernard Chazelle, Ding Liu
2001 Proceedings of the thirty-third annual ACM symposium on Theory of computing - STOC '01  
Does any convex polytope have a boundary dominant Dobkin-Kirkpatrick hierarchy? Can fractional cascading be generalized to planar maps instead of linear lists?  ...  If the query is a plane and the input is a polytope with n vertices, can one achieve Oðk þ polylogðnÞÞ time with subcubic storage?  ...  Introduction Fractional cascading is a general technique for speeding up lookup queries in catalogs associated with the nodes of a graph [14] .  ... 
doi:10.1145/380752.380818 dblp:conf/stoc/ChazelleL01 fatcat:qr6xnf23jzfmdnglqzddx46bpa
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