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Storing a Sparse Table with 0(1) Worst Case Access Time

Michael L. Fredman, János Komlós, Endre Szemerédi
1984 Journal of the ACM  
A data structure for representing a set of n items from a umverse of m items, which uses space n + o(n) and accommodates membership queries m constant time is described.  ...  This sequence of probes can be adaptive: The Storing a Sparse Table with 0(1) Worst Case Access Time 539 next cell to be probed is determined precisely by q and the contents of the cells previously probed  ...  A second table A[j], ,j E I, is used to store offsets: A[j] = 0 if Wj = ~, otherwise B[a] + A[j] is the address in T' associated with ~ forj E ~.  ... 
doi:10.1145/828.1884 fatcat:hhvmasid2faelgzej4kh5xbcj4

High-speed Firewall Rule Verification with O(1) Worst-case Access Time

Suchart Khummanee, Kitt Tientanopajai
2017 International Journal of Network Security  
In this paper, we have presented several techniques to improve the speed of firewall rule verification with O(1) worstcase access time.  ...  Firewalls enforced by rules are a security measure for verifying huge packets at gateway networks. Therefore, they probably act as bottlenecks of the networks.  ...  However, provided that the operation has known the in-dex of i and j to access an element in the matrix, the worst-case access time will be O(1). Sparse matrix storage formats.  ... 
dblp:journals/ijnsec/KhummaneeT17 fatcat:jumhbxubfjgczifbbyidve6oj4

Space Efficient Hash Tables with Worst Case Constant Access Time [chapter]

Dimitris Fotakis, Rasmus Pagh, Peter Sanders, Paul Spirakis
2003 Lecture Notes in Computer Science  
This is the first dictionary that has worst case constant access time and expected constant update time, works with (1 + ε) n space, and supports satellite information.  ...  We generalize Cuckoo Hashing [23] to d-ary Cuckoo Hashing and show how this yields a simple hash table data structure that stores n elements in (1 + ε) n memory cells, for any constant ε > 0.  ...  The main contribution of this paper is a hash table data structure with worst case constant access time and memory consumption only (1+ε) n.  ... 
doi:10.1007/3-540-36494-3_25 fatcat:55hp4pjbvbh7xiqpkatvdvefvy

Space Efficient Hash Tables with Worst Case Constant Access Time

Dimitris Fotakis, Rasmus Pagh, Peter Sanders, Paul Spirakis
2004 Theory of Computing Systems  
This is the first dictionary that has worst case constant access time and expected constant update time, works with (1 + ε) n space, and supports satellite information.  ...  We generalize Cuckoo Hashing [23] to d-ary Cuckoo Hashing and show how this yields a simple hash table data structure that stores n elements in (1 + ε) n memory cells, for any constant ε > 0.  ...  The main contribution of this paper is a hash table data structure with worst case constant access time and memory consumption only (1+ε) n.  ... 
doi:10.1007/s00224-004-1195-x fatcat:jjt7kabgefdptn567emefekn2m

Low Redundancy in Static Dictionaries with O(1) Worst Case Lookup Time [chapter]

Rasmus Pagh
1999 Lecture Notes in Computer Science  
We study this problem in a unit cost RAM model with word size Ω(log |U |), and show that for n-element subsets, constant worst case query time can be obtained using B + O(log log |U |) + o(n) bits of storage  ...  For |U | = n log O(1) n the dictionary supports constant time rank queries.  ...  For m = n log O(1) n, a static rank dictionary with worst case constant query time can be represented using B + O( n log 2 log n log n ) bits.  ... 
doi:10.1007/3-540-48523-6_56 fatcat:hzh6za2hqjfh7oaohpbijerxny

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

Rasmus Pagh
1998 BRICS Report Series  
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  ...  A static dictionary is a data structure for storing subsets of a finite universe U, so that membership queries can be answered efficiently.  ...  Setting b = c = α log m, for some 0 < α < 1 we get the following: Theorem 2 A static rank dictionary with worst case constant query time, can be represented using B + O( m log log m log m ) bits.  ... 
doi:10.7146/brics.v5i28.19434 fatcat:dy3khwebfjg3hmbwopqebg5gc4

Revisiting Sparse Dynamic Programming for the 0/1 Knapsack Problem

Tarequl Islam Sifat, Nirmal Prajapati, Sanjay Rajopadhye
2020 49th International Conference on Parallel Processing - ICPP  
REVISITING SPARSE DYNAMIC PROGRAMMING FOR THE 0/1 KNAPSACK PROBLEM The 0/1-Knapsack Problem is a classic NP-hard problem.  ...  A socalled, "sparse" DP algorithm (SKPDP) that performs fewer operations than the standard algorithm (KPDP) is well known.  ...  In the worst case, a problem instance will hardly have any sparsity and, therefore, most of the rows in the sparse table will be of length C.  ... 
doi:10.1145/3404397.3404462 dblp:conf/icpp/SifatPR20 fatcat:qlgzble6jnfsddr3yanf4c4i6y

A Simplified Description of Child Tables for Sequence Similarity Search

Martin Frith, Anish Shrestha
2018 IEEE/ACM Transactions on Computational Biology & Bioinformatics  
In any case, we then seek sequence segment-pairs with high model-likelihood of being related.  ...  This paper aims to provide a more accessible description of child tables, and demonstrate their generality: they apply equally to all the above-mentioned seed types and more.  ...  The original child table breaks ties by choosing the first minimum [15] , which leads to worst-case search time proportional to the alphabet size.  ... 
doi:10.1109/tcbb.2018.2796064 pmid:29994365 fatcat:gvpmuoic7vetrcdonghl5f3qpu

A Dynamic Space-Efficient Filter with Constant Time Operations

Ioana O. Bercea, Guy Even, Susanne Albers
2020 Scandinavian Workshop on Algorithm Theory  
For the case that log(1/ε) = O(log log n), we present the first space-efficient dynamic filter with constant time operations in the worst case (whp).  ...  The goal is to obtain dynamic filters that are space-efficient (the space is 1+o(1) times the information-theoretic lower bound) and support all operations in constant time with high probability.  ...  The proof of Thm. 1 deals with the sparse case and dense case separately. The theorem for the sparse case, in which log(1/ε) = ω(log log n), is proven in Sec. 6 .  ... 
doi:10.4230/lipics.swat.2020.11 dblp:conf/swat/BerceaE20 fatcat:xd4z4ultsva4periughzglub2u

Faster range minimum queries [article]

Tomasz Kowalski, Szymon Grabowski
2017 arXiv   pre-print
We subsequently refine our technique, combining it with one of the existing succinct solutions with O(1) worst-case time queries and no access to the input array.  ...  In this work, we present a simple data structure, with very fast construction, which allows to handle queries in constant time on average.  ...  As a next solution we thus proposed to combine our technique with one of the existing succinct solutions with O(1) worst-case time queries and no access to the input array.  ... 
arXiv:1711.10385v1 fatcat:civqumrk3fb3xo2lwjfz4rmxye

Fast address lookups using controlled prefix expansion

V. Srinivasan, G. Varghese
1999 ACM Transactions on Computer Systems  
On a 300MHz Pentium II which takes 4 cycles for accessing the first word of the L2 cacheline, this algorithm has a worst-case search time of 180 nsec., a worst-case insert/delete time of 2.5 msec., and  ...  When applied to Binary Search on Levels, our techniques improve worst-case search times by nearly a factor of 2 (using twice as much storage) for the MaeEast database.  ...  Assume each node has a 0-pointer and a 0-info field, and similarly a 1-pointer and 1-info field.  ... 
doi:10.1145/296502.296503 fatcat:zpxuj3ftivhdvi2ccmk6hpbauq

Static analysis of the worst-case memory performance for irregular codes with indirections

Diego Andrade, Basilio B. Fraguela, Ramón Doallo
2012 ACM Transactions on Architecture and Code Optimization (TACO)  
Real-time systems are subject to timing constraints, whose upper bound is given by the Worst-Case Execution Time (WCET).  ...  The worst-case memory performance (WCMP) component of the WCET can only be estimated with the precise knowledge of the stream of data addresses accessed by the code, which is determined by the access patterns  ...  Figure 3 , case (a), shows the sparse matrix that produces this kind of worst-case access pattern in the accesses to vector x.  ... 
doi:10.1145/2355585.2355593 fatcat:q7dojf3qgjgbhisnmpk4pnhjzy

DACs: Bringing direct access to variable-length codes

Nieves R. Brisaboa, Susana Ladra, Gonzalo Navarro
2013 Information Processing & Management  
We show some experiments demonstrating that the technique is not only simple, but also competitive in time and space with existing solutions in several applications, such as the representation of LCP arrays  ...  We present a new variable-length encoding scheme for sequences of integers, Directly Addressable Codes (DACs), which enables direct access to any element of the encoded sequence without the need of any  ...  Acknowledgments This work was founded in part by MCIN grant TIN2009-14560-C03-02 and CDTI CEN-20091048, and Xunta de Galicia grant 2010/17 (for the first and second authors), and Fondecyt grant 1-110066  ... 
doi:10.1016/j.ipm.2012.08.003 fatcat:nshc4t7qsvf7laqyihd4y5qgia

Solving structured nonsmooth convex optimization with complexity $$\mathcal {O}(\varepsilon ^{-1/2})$$ O ( ε - 1 / 2 )

Masoud Ahookhosh, Arnold Neumaier
2017 TOP - An Official Journal of the Spanish Society of Statistics and Operations Research  
If the nonsmoothness of the problem is manifested in a structured way, we reformulate the problem so that it can be solved efficiently by a new setup of OSGA (called OSGA-V) with the complexity O(ε −1/  ...  ) for Lipschitz continuous nonsmooth problems and O(ε −1/2 ) for smooth problems with Lipschitz continuous gradient.  ...  We are very thankful to anonymous referees for a careful reading and many useful suggestions, which improved the paper.  ... 
doi:10.1007/s11750-017-0462-3 fatcat:y7lzfuoqhfg55abt3pybnu6icu

A sparse table implementation of priority queues [chapter]

Alon Itai, Alan G. Konheim, Michael Rodeh
1981 Lecture Notes in Computer Science  
To improve the worst case behavior, a more complicated sparse table scheme is introduced in Section 5 which requires no more than O(n log 2n) time to build up a table with n elements.  ...  To improve the worst case performance an additional structure is imposed on the sparse table, yielding a more complicated scheme which we refer to as the hierarchical sparse table.  ... 
doi:10.1007/3-540-10843-2_34 fatcat:24idhcybq5badj56uvqnbx4kfy
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