On the Use of Inaccessible Numbers and Order Indiscernibles in Lower Bound Arguments for Random Access Machines

1988 ◽  
Vol 53 (4) ◽  
pp. 1098 ◽  
Author(s):  
Wolfgang Maass
Keyword(s):  
Lower Bound ◽  
Random Access

scholarly journals Lower Bounds for Dynamic Transitive Closure, Planar Point Location, and Parentheses Matching

1996 ◽  
Vol 3 (9) ◽  
Author(s):  
Thore Husfeldt ◽  
Theis Rauhe ◽  
Søren Skyum
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Transitive Closure ◽  
Unit Cost ◽  
Random Access ◽  
Point Location ◽  
Worst Case ◽  
Planar Point ◽  
Planar Point Location ◽  
Prefix Sums

We give a number of new lower bounds in the cell probe model<br />with logarithmic cell size, which entails the same bounds on the random access computer with logarithmic word size and unit cost operations. We study the signed prefix sum problem: given a string of length n of zeroes and signed ones, compute the sum of its ith prefix during updates. We show a<br />lower bound of  Omega(log n/log log n) time per operations, even if the prefix sums are bounded by log n/log log n during all updates. We also show that if the update time is bounded by the product of the worst-case update time and the<br />answer to the query, then the update time must be Omega(sqrt(log n/ log log n)).<br /> These results allow us to prove lower bounds for a variety of seemingly unrelated<br />dynamic problems. We give a lower bound for the dynamic planar point location in monotone subdivisions of <br />Omega(log n/ log log n) per operation. We give<br />a lower bound for the dynamic transitive closure problem on upward planar graphs with one source and one sink of <br />Omega(log n/(log logn)^2) per operation. We give a lower bound of  Omega(sqrt(log n/log log n)) for the dynamic membership problem of any Dyck language with two or more letters. This implies the same<br />lower bound for the dynamic word problem for the free group with k generators. We also give lower bounds for the dynamic prefix majority and prefix equality problems.

scholarly journals Lower bound for average delay in unblocked random access algorithm with orthogonal preambles

2020 ◽  
pp. 79-85
Author(s):  
Artem Burkov ◽  
Seva Shneer ◽  
Andrey Turlikov
Keyword(s):  
Lower Bound ◽  
Resource Sharing ◽  
Queuing Theory ◽  
Multiple Access ◽  
System Analysis ◽  
Random Access ◽  
Arrival Rate ◽  
High Energy ◽  
Average Delay ◽  
Closed Expression

Introduction: Currently, the first versions of 5G communication standard networks are being deployed and discussions are underway on the further development of cellular networks and the transition to the 6G standard. The work of the currently popular idea of ​​the Internet of Things (IoT) is supposed to be in the framework of a Massive Machine-Type Communications scenario, which has a number of requirements for operation characteristics: very high energy efficiency, relatively low delay and fairly reliable communication. It is assumed that random multiple access procedures are used, since, due to the nature of the traffic, it is impossible to develop a channel resource sharing policy. To increase the efficiency of random access, a class of unblocked algorithms using orthogonal preambles can be used. Purpose: to calculate the lower bound of the average delay for the class of unblocked random multiple access algorithms using orthogonal preambles. Methods: system analysis, a theory of random processes, queuing theory, and simulation. Results: A model of a system with a potentially unlimited number of users who use random unblocked access to transmit data over a common communication channel using orthogonal preambles is proposed. A closed expression is obtained for calculating the lower bound of the average delay in such a system depending on the intensity of the input arrival rate. The limit value of the intensity of the input arrival rate to which the system operates stably is determined. Shown are the results of simulation with respect to the obtained bound. Practical relevance: the obtained boundary allows us to estimate the lower average delay in the described class of algorithms. Its application allows us to determine the possibility of using the considered class of algorithms from the point of view of limitations on the average delay at the stage of designing random multiple access systems.

On the use of inaccessible numbers and order indiscernibles in lower bound arguments for random access machines

1988 ◽  
Vol 53 (4) ◽  
pp. 1098-1109 ◽  
Author(s):  
Wolfgang Maass
Keyword(s):  
Mathematical Logic ◽  
Lower Bound ◽  
Computational Model ◽  
Lower Bounds ◽  
Special Interest ◽  
Random Access ◽  
Computation Time ◽  
Test Problems ◽  
Random Access Machine

AbstractWe prove optimal lower bounds on the computation time for several well-known test problems on a quite realistic computational model: the random access machine. These lower bound arguments may be of special interest for logicians because they rely on finitary analogues of two important concepts from mathematical logic: inaccessible numbers and order indiscernibles.

scholarly journals Memory-Adjustable Navigation Piles with Applications to Sorting and Convex Hulls

2021 ◽  
Vol 17 (2) ◽  
pp. 1-19
Author(s):  
Omar Darwish ◽  
Amr Elmasry ◽  
Jyrki Katajainen
Keyword(s):  
Data Structure ◽  
Lower Bound ◽  
Convex Hull ◽  
Euclidean Plane ◽  
State Of The Art ◽  
Random Access ◽  
Priority Queue ◽  
Convex Hulls ◽  
Limited Capacity ◽  
Range Of Values

We consider space-bounded computations on a random-access machine, where the input is given on a read-only random-access medium, the output is to be produced to a write-only sequential-access medium, and the available workspace allows random reads and writes but is of limited capacity. The length of the input is N elements, the length of the output is limited by the computation, and the capacity of the workspace is O ( S ) bits for some predetermined parameter S ≥ lg N . We present a state-of-the-art priority queue—called an adjustable navigation pile —for this restricted model. This priority queue supports M inimum in O (1) time, C onstruct in O ( N ) time, and E xtract - min in O ( N / S + lg S ) time for any S ≥ lg N . The priority queue can be further augmented in O ( N ) time to deal with a batch of at most S elements in a specified range of values at a time, and allow to I nsert (activate) or E xtract (deactivate) an element among these elements, such that I nsert and E xtract take O ( N / S + lg S ) time for any S ≥ lg N . We show how to use our data structure to sort N elements and to compute the convex hull of N points in the Euclidean plane in O ( N 2 / S + N lg S ) time for any S ≥ lg N . Following a known lower bound for the space-time product of any branching program for finding unique elements, both our sorting and convex-hull algorithms are optimal. The adjustable navigation pile has turned out to be useful when designing other space-efficient algorithms, and we expect that it will find its way to yet other applications.

Modern Random Access Protocols

2016 ◽  
Author(s):  
Matteo Berioli ◽  
Giuseppe Cocco ◽  
Gianluigi Liva ◽  
Andrea Munari
Keyword(s):  
Random Access ◽  
Access Protocols
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