Average case lower bounds on the construction and searching of partial orders

2014 ◽

Vol 91 (1) ◽

pp. 104-115 ◽

Cited By ~ 1

Author(s):

SUREEPORN CHAOPRAKNOI ◽

TEERAPHONG PHONGPATTANACHAROEN ◽

PONGSAN PRAKITSRI

Keyword(s):

Semigroup Forum ◽

Partial Order ◽

Lower Bounds ◽

Partial Orders ◽

Natural Partial Order ◽

Linear Transformations ◽

Bounded Below

AbstractHiggins [‘The Mitsch order on a semigroup’, Semigroup Forum 49 (1994), 261–266] showed that the natural partial orders on a semigroup and its regular subsemigroups coincide. This is why we are interested in the study of the natural partial order on nonregular semigroups. Of particular interest are the nonregular semigroups of linear transformations with lower bounds on the nullity or the co-rank. In this paper, we determine when they exist, characterise the natural partial order on these nonregular semigroups and consider questions of compatibility, minimality and maximality. In addition, we provide many examples associated with our results.

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ON THE AVERAGE CASE CIRCUIT DELAY OF DISJUNCTION

Parallel Processing Letters ◽

10.1142/s0129626495000254 ◽

1995 ◽

Vol 05 (02) ◽

pp. 275-280 ◽

Cited By ~ 2

Author(s):

BEATE BOLLIG ◽

MARTIN HÜHNE ◽

STEFAN PÖLT ◽

PETR SAVICKÝ

Keyword(s):

Lower Bounds ◽

Wide Class ◽

Time Complexity ◽

Upper And Lower Bounds ◽

Average Case ◽

Asymptotically Optimal ◽

Circuit Delay ◽

Suitable Measure

For circuits the expected delay is a suitable measure for the average case time complexity. In this paper, new upper and lower bounds on the expected delay of circuits for disjunction and conjunction are derived. The circuits presented yield asymptotically optimal expected delay for a wide class of distributions on the inputs even when the parameters of the distribution are not known in advance.

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Improved Average-Case Lower Bounds for DeMorgan Formula Size

2013 IEEE 54th Annual Symposium on Foundations of Computer Science ◽

10.1109/focs.2013.69 ◽

2013 ◽

Cited By ~ 19

Author(s):

Ilan Komargodski ◽

Ran Raz ◽

Avishay Tal

Keyword(s):

Lower Bounds ◽

Average Case

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BOUNDS AND PERFORMANCE LIMITS OF CHANNEL ASSIGNMENT POLICIES IN CELLULAR NETWORKS

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964802161067 ◽

2002 ◽

Vol 16 (1) ◽

pp. 85-100

Author(s):

Nicole Bäuerle ◽

Anja Houdek

Keyword(s):

Cellular Networks ◽

Lower Bounds ◽

Channel Assignment ◽

Linear Program ◽

Performance Limits ◽

Average Case ◽

Interference Graph ◽

Deterministic Control ◽

Fixed Channel Assignment ◽

And Performance

We investigate the performance of channel assignment policies for cellular networks. The networks are given by an interference graph which describes the reuse constraints for the channels. In the first part, we derive lower bounds on the expected (weighted) number of blocked calls under any channel assignment policy over finite time intervals as well as in the average case. The lower bounds are solutions of deterministic control problems. As far as the average case is concerned, the control problem can be replaced by a linear program. In the second part, we consider the cellular network in the limit, when the number of available channels as well as the arrival intensities are linearly increased. We show that the network obeys a functional law of large numbers and that a fixed channel assignment policy which can be computed from a linear program is asymptotically optimal. Special networks like fully connected and star networks are considered.

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The stretch-length tradeoff in geometric networks: average case and worst case study

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004115000250 ◽

2015 ◽

Vol 159 (1) ◽

pp. 125-151

Author(s):

DAVID ALDOUS ◽

TAMAR LANDO

Keyword(s):

Lower Bounds ◽

Poisson Point Process ◽

Euclidean Distance ◽

Unit Area ◽

Average Density ◽

Upper And Lower Bounds ◽

Worst Case ◽

Average Case ◽

Route Length

AbstractConsider a network linking the points of a rate-1 Poisson point process on the plane. Write Ψave(s) for the minimum possible mean length per unit area of such a network, subject to the constraint that the route-length between every pair of points is at moststimes the Euclidean distance. We give upper and lower bounds on the function Ψave(s), and on the analogous “worst-case” function Ψworst(s) where the point configuration is arbitrary subject to average density one per unit area. Our bounds are numerically crude, but raise the question of whether there is an exponent α such that each function has Ψ(s) ≍ (s− 1)−αass↓ 1.

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