scholarly journals A Selectable Sloppy Heap

Algorithms ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 58 ◽  
Author(s):  
Adrian Dumitrescu
Keyword(s):  
Data Structure ◽  
Upper Bounds ◽  
Structure Design ◽  
Constant Time ◽  
Worst Case ◽  
Slowing Down ◽  
Insertion And Deletion ◽  
Speed Up ◽  
Amortized Complexity ◽  
Dynamic Version

We study the selection problem, namely that of computing the ith order statistic of n given elements. Here we offer a data structure called selectable sloppy heap that handles a dynamic version in which upon request (i) a new element is inserted or (ii) an element of a prescribed quantile group is deleted from the data structure. Each operation is executed in constant time—and is thus independent of n (the number of elements stored in the data structure)—provided that the number of quantile groups is fixed. This is the first result of this kind accommodating both insertion and deletion in constant time. As such, our data structure outperforms the soft heap data structure of Chazelle (which only offers constant amortized complexity for a fixed error rate 0 < ε ≤ 1 / 2 ) in applications such as dynamic percentile maintenance. The design demonstrates how slowing down a certain computation can speed up the data structure. The method described here is likely to have further impact in the field of data structure design in extending asymptotic amortized upper bounds to same formula asymptotic worst-case bounds.

scholarly journals Encoding range minima and range top-2 queries

2014 ◽  
Vol 372 (2016) ◽  
pp. 20130131 ◽  
Author(s):  
Pooya Davoodi ◽  
Gonzalo Navarro ◽  
Rajeev Raman ◽  
S. Srinivasa Rao
Keyword(s):  
Data Structure ◽  
Lower Bounds ◽  
Query Time ◽  
Constant Time ◽  
Worst Case ◽  
Asymptotically Optimal ◽  
Random Array ◽  
Case Data ◽  
Natural Way

We consider the problem of encoding range minimum queries (RMQs): given an array A [1.. n ] of distinct totally ordered values, to pre-process A and create a data structure that can answer the query RMQ( i , j ), which returns the index containing the smallest element in A [ i .. j ], without access to the array A at query time. We give a data structure whose space usage is 2 n + o ( n ) bits, which is asymptotically optimal for worst-case data, and answers RMQs in O (1) worst-case time. This matches the previous result of Fischer and Heun, but is obtained in a more natural way. Furthermore, our result can encode the RMQs of a random array A in 1.919 n + o ( n ) bits in expectation, which is not known to hold for Fischer and Heun’s result. We then generalize our result to the encoding range top-2 query (RT2Q) problem, which is like the encoding RMQ problem except that the query RT2Q( i , j ) returns the indices of both the smallest and second smallest elements of A [ i .. j ]. We introduce a data structure using 3.272 n + o ( n ) bits that answers RT2Qs in constant time, and also give lower bounds on the effective entropy of the RT2Q problem.

scholarly journals d-PBWT: dynamic positional Burrows-Wheeler transform

2020 ◽  
Author(s):  
Ahsan Sanaullah ◽  
Degui Zhi ◽  
Shaojie Zhang
Keyword(s):  
Data Structure ◽  
Time Complexity ◽  
Linear Time ◽  
Genotype Imputation ◽  
Worst Case ◽  
Average Case ◽  
Insertion And Deletion ◽  
Static Data ◽  
Efficient Retrieval ◽  
Burrows Wheeler Transform

AbstractDurbin’s PBWT, a scalable data structure for haplotype matching, has been successfully applied to identical by descent (IBD) segment identification and genotype imputation. Once the PBWT of a haplotype panel is constructed, it supports efficient retrieval of all shared long segments among all individuals (long matches) and efficient query between an external haplotype and the panel. However, the standard PBWT is an array-based static data structure and does not support dynamic updates of the panel. Here, we generalize the static PBWT to a dynamic data structure, d-PBWT, where the reverse prefix sorting at each position is represented by linked lists. We developed efficient algorithms for insertion and deletion of individual haplotypes. In addition, we verified that d-PBWT can support all algorithms of PBWT. In doing so, we systematically investigated variations of set maximal match and long match query algorithms: while they all have average case time complexity independent of database size, they have different worst case complexities, linear time complexity with the size of the genome, and dependency on additional data structures.

Dynamic Generalized Suffix Arrays

2012 ◽  
Vol 263-266 ◽  
pp. 1398-1401
Author(s):  
Song Feng Lu ◽  
Hua Zhao
Keyword(s):  
Data Structure ◽  
Pattern Matching ◽  
Time Complexity ◽  
Document Retrieval ◽  
Suffix Array ◽  
Index Structure ◽  
Suffix Arrays ◽  
Basic Task ◽  
Insertion And Deletion ◽  
Dynamic Version

Document retrieval is the basic task of search engines, and seize amount of attention by the pattern matching community. In this paper, we focused on the dynamic version of this problem, in which the text insertion and deletion is allowable. By using the generalized suffix array and other data structure, we proposed a new index structure. Our scheme achieved better time complexity than the existing ones, and a bit more space overhead is needed as return.

scholarly journals Low Redundancy in Dictionaries with O(1) Worst Case Lookup Time

1998 ◽  
Vol 5 (28) ◽  
Author(s):  
Rasmus Pagh
Keyword(s):  
Data Structure ◽  
Unit Cost ◽  
Query Time ◽  
Constant Time ◽  
Worst Case ◽  
Insertions And Deletions ◽  
Word Size ◽  
Membership Queries ◽  
Dynamic Setting ◽  
Minimum Number

A static dictionary is a data structure for storing subsets of a finite universe U, so that membership queries can be answered efficiently. We study this problem in a unit cost RAM model with word size  Omega(log |U|), and show that for n-element subsets,<br />constant worst case query time can be obtained using B +O(log log |U|)+o(n) bits of storage, where B = [log2 (|U| / n)]<br />is the minimum number of bits needed to represent all<br />such subsets. The solution for dense subsets uses B + O( |U| log log |U| / log |U| ) bits of storage, and supports constant time rank queries. In a dynamic setting, allowing insertions and deletions, our techniques give an O(B) bit space usage.

scholarly journals DYNAMIZATION OF THE TRAPEZOID METHOD FOR PLANAR POINT LOCATION IN MONOTONE SUBDIVISIONS

1992 ◽  
Vol 02 (03) ◽  
pp. 311-333 ◽  
Author(s):  
YI-JEN CHIANG ◽  
ROBERTO TAMASSIA
Keyword(s):  
Data Structure ◽  
Point Location ◽  
Worst Case ◽  
Dynamic Data ◽  
Location Data ◽  
Insertion And Deletion ◽  
Planar Point Location ◽  
Vertex Insertion ◽  
Trapezoid Method ◽  
Dynamic Data Structure

We present a fully dynamic data structure for point location in a monotone subdivision, based on the trapezoid method. The operations supported are insertion and deletion of vertices and edges, and horizontal translation of vertices. Let n be the current number of vertices of the subdivision. Point location queries take O( log n) time, while updates take O ( log 2 n) time (amortized for vertex insertion/deletion and worst-case for the other updates). The space requirement is O(n log n). This is the first fully dynamic point location data structure for monotone subdivisions that achieves optimal query time.

M-Heap: A Modified Heap Data Structure

2003 ◽  
Vol 14 (03) ◽  
pp. 491-502 ◽  
Author(s):  
S. Bansal ◽  
S. Sreekanth ◽  
P. Gupta
Keyword(s):  
Data Structure ◽  
Constant Time ◽  
Similar Time ◽  
Insertion And Deletion ◽  
Time Bounds

In this paper a new data structure named M-heaps is proposed. This data structure is a modification of the well known binary heap data structure. The new structure supports insertion in constant time and deletion in O(log n) time. Finally a generalization of the data structure to d – ary M-heaps is presented. This structure has similar time-bounds for insertion and deletion.

scholarly journals d-PBWT: dynamic positional Burrows-Wheeler transform

2021 ◽  
Author(s):  
Ahsan Sanaullah ◽  
Degui Zhi ◽  
Shaojie Zhang
Keyword(s):  
Data Structure ◽  
Genotype Imputation ◽  
Supplementary Information ◽  
Worst Case ◽  
Average Case ◽  
Insertion And Deletion ◽  
Static Data ◽  
Efficient Retrieval ◽  
Dynamic Data Structure ◽  
Burrows Wheeler Transform

Abstract Motivation Durbin’s positional Burrows-Wheeler transform (PBWT) is a scalable data structure for haplotype matching. It has been successfully applied to identical by descent (IBD) segment identification and genotype imputation. Once the PBWT of a haplotype panel is constructed, it supports efficient retrieval of all shared long segments among all individuals (long matches) and efficient query between an external haplotype and the panel. However, the standard PBWT is an array-based static data structure and does not support dynamic updates of the panel. Results Here, we generalize the static PBWT to a dynamic data structure, d-PBWT, where the reverse prefix sorting at each position is stored with linked lists.We also developed efficient algorithms for insertion and deletion of individual haplotypes. In addition, we verified that d-PBWT can support all algorithms of PBWT. In doing so, we systematically investigated variations of set maximal match and long match query algorithms: while they all have average case time complexity independent of database size, they have different worst case complexities and dependencies on additional data structures. Availability The benchmarking code is available at genome.ucf.edu/d-PBWT. Supplementary information Supplementary Materials are available at Bioinformatics online.

scholarly journals Temporal concatenation for Markov decision processes

2021 ◽  
pp. 1-28
Author(s):  
Ruiyang Song ◽  
Kuang Xu
Keyword(s):  
Markov Decision Processes ◽  
Large Scale ◽  
Optimal Solution ◽  
Upper Bounds ◽  
Black Box ◽  
Decision Processes ◽  
Optimal Solutions ◽  
Wide Range ◽  
Markov Decision ◽  
Speed Up

We propose and analyze a temporal concatenation heuristic for solving large-scale finite-horizon Markov decision processes (MDP), which divides the MDP into smaller sub-problems along the time horizon and generates an overall solution by simply concatenating the optimal solutions from these sub-problems. As a “black box” architecture, temporal concatenation works with a wide range of existing MDP algorithms. Our main results characterize the regret of temporal concatenation compared to the optimal solution. We provide upper bounds for general MDP instances, as well as a family of MDP instances in which the upper bounds are shown to be tight. Together, our results demonstrate temporal concatenation's potential of substantial speed-up at the expense of some performance degradation.

scholarly journals Interregional Transfers for Pandemic Surges

2020 ◽  
Author(s):  
Kenneth A Michelson ◽  
Chris A Rees ◽  
Jayshree Sarathy ◽  
Paige VonAchen ◽  
Michael Wornow ◽  
...  
Keyword(s):  
The United States ◽  
Upper Bounds ◽  
Hospital Inpatient ◽  
Worst Case ◽  
Icu Patients ◽  
Interregional Transfers ◽  
Number Of Patients ◽  
Bed Capacity ◽  
Model Scenarios ◽  
Do So

Abstract Background Hospital inpatient and intensive care unit (ICU) bed shortfalls may arise due to regional surges in volume. We sought to determine how interregional transfers could alleviate bed shortfalls during a pandemic. Methods We used estimates of past and projected inpatient and ICU cases of coronavirus disease 2019 (COVID-19) from 4 February 2020 to 1 October 2020. For regions with bed shortfalls (where the number of patients exceeded bed capacity), transfers to the nearest region with unused beds were simulated using an algorithm that minimized total interregional transfer distances across the United States. Model scenarios used a range of predicted COVID-19 volumes (lower, mean, and upper bounds) and non–COVID-19 volumes (20%, 50%, or 80% of baseline hospital volumes). Scenarios were created for each day of data, and worst-case scenarios were created treating all regions’ peak volumes as simultaneous. Mean per-patient transfer distances were calculated by scenario. Results For the worst-case scenarios, national bed shortfalls ranged from 669 to 58 562 inpatient beds and 3208 to 31 190 ICU beds, depending on model volume parameters. Mean transfer distances to alleviate daily bed shortfalls ranged from 23 to 352 miles for inpatient and 28 to 423 miles for ICU patients, depending on volume. Under all worst-case scenarios except the highest-volume ICU scenario, interregional transfers could fully resolve bed shortfalls. To do so, mean transfer distances would be 24 to 405 miles for inpatients and 73 to 476 miles for ICU patients. Conclusions Interregional transfers could mitigate regional bed shortfalls during pandemic hospital surges.

Experimental Study on the Dynamic Deformation of Simply Supported Beam in Chinese High-speed Railway

2018 ◽  
Author(s):  
Gonglian Dai ◽  
Meng Wang ◽  
Tianliang Zhao ◽  
Wenshuo Liu
Keyword(s):  
High Speed ◽  
Structure Design ◽  
Dynamic Coefficient ◽  
Bridge Structure ◽  
High Speed Railway ◽  
Simply Supported Beam ◽  
Vertical Stiffness ◽  
Simply Supported ◽  
Speed Up ◽  
Design Speed

<p>At present, Chinese high-speed railway operating mileage has exceeded 20 thousand km, and the proportion of the bridge is nearly 50%. Moreover, high-speed railway design speed is constantly improving. Therefore, controlling the deformation of the bridge structure strictly is particularly important to train speed-up as well as to ensure the smoothness of the line. This paper, based on the field test, shows the vertical and transverse absolute displacements of bridge structure by field collection. What’s more, resonance speed and dynamic coefficient of bridge were studied. The results show that: the horizontal and vertical stiffness of the bridge can meet the requirements of <b>Chinese “high-speed railway design specification” (HRDS)</b>, and the structure design can be optimized. However, the dynamic coefficient may be greater than the specification suggested value. And the simply supported beam with CRTSII ballastless track has second-order vertical resonance velocity 306km/h and third-order transverse resonance velocity 312km/h by test results, which are all coincide with the theoretical resonance velocity.</p>

Sign in / Sign up

Export Citation Format

Share Document