scholarly journals Convex Partitions of Polyhedra: A Lower Bound and Worst-Case Optimal Algorithm

1984 ◽  
Vol 13 (3) ◽  
pp. 488-507 ◽  
Author(s):  
Bernard Chazelle
Keyword(s):  
Lower Bound ◽  
Optimal Algorithm ◽  
Worst Case ◽  
Convex Partitions

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 State Complexity of Neighbourhoods and Approximate Pattern Matching

2018 ◽  
Vol 29 (02) ◽  
pp. 315-329 ◽  
Author(s):  
Timothy Ng ◽  
David Rappaport ◽  
Kai Salomaa
Keyword(s):  
Lower Bound ◽  
Pattern Matching ◽  
Finite Automaton ◽  
The State ◽  
Worst Case ◽  
State Complexity ◽  
Approximate Pattern Matching ◽  
The Given ◽  
Nondeterministic Finite Automaton ◽  
Distance Formula

The neighbourhood of a language [Formula: see text] with respect to an additive distance consists of all strings that have distance at most the given radius from some string of [Formula: see text]. We show that the worst case deterministic state complexity of a radius [Formula: see text] neighbourhood of a language recognized by an [Formula: see text] state nondeterministic finite automaton [Formula: see text] is [Formula: see text]. In the case where [Formula: see text] is deterministic we get the same lower bound for the state complexity of the neighbourhood if we use an additive quasi-distance. The lower bound constructions use an alphabet of size linear in [Formula: see text]. We show that the worst case state complexity of the set of strings that contain a substring within distance [Formula: see text] from a string recognized by [Formula: see text] is [Formula: see text].

A UNIFIED ALGORITHM FOR THE ESTIMATION AND SCHEDULING OF DATA FLOW GRAPHS

1996 ◽  
Vol 06 (03) ◽  
pp. 287-318 ◽  
Author(s):  
YUAN HU ◽  
BRADLEY S. CARLSON
Keyword(s):  
Lower Bound ◽  
Data Flow ◽  
Optimal Algorithm ◽  
Solution Space ◽  
Computation Time ◽  
Upper And Lower Bounds ◽  
Unified Algorithm ◽  
Data Flow Graphs ◽  
Flow Graphs ◽  
Sharp Lower Bound

A unified algorithm is presented to solve the problem of estimation and scheduling for performance constrained data flow graphs. The algorithm achieves superior results by first computing a lower bound on the number of functional units required to satisfy the performance constraint T, and then scheduling the operations into the best control steps using the lower bound algorithm. The lower bound not only greatly reduces the size of the solution space, but also provides a means to measure the proximity of the final solution to an optimal one. Our algorithm is the first one to use a sharp lower bound estimation technique to direct scheduling. In addition, our unified algorithm can easily be incorporated into a branch-and-bound algorithm to solve the scheduling problem optimally. Since our algorithm computes a sharp lower bound, the computation time of an optimal algorithm can be greatly reduced. Experiments indicate that our scheduling algorithm can produce results very close to the lower bound. For all of the test cases the difference between our upper and lower bounds is not greater than one.

ON THE LOWER BOUND OF THE COMPETITIVE RATIO FOR THE WEIGHTED ONLINE ROOMMATES PROBLEM

2010 ◽  
Vol 02 (02) ◽  
pp. 257-262
Author(s):  
SATYAJIT BANERJEE
Keyword(s):  
Lower Bound ◽  
Competitive Ratio ◽  
Deterministic Algorithm ◽  
Weighted Version ◽  
Worst Case ◽  
Competitive Algorithm

We show that the best possible worst case competitive ratio of any deterministic algorithm for weighted online roommates problem is arbitrarily close to 4. This proves that the 4-competitive algorithm proposed by Bernstein and Rajagopalan [3] for the weighted version of the online roommates problem actually attains the best possible competitive ratio.

A Game Theoretic Approach to Multi-Period Newsvendor Problems with Censored Markovian Demand

2019 ◽  
Vol 01 (01) ◽  
Author(s):  
Farzaneh Mansourifard ◽  
Parisa Mansourifard ◽  
Bhaskar Krishnamachari
Keyword(s):  
Lower Bound ◽  
Convex Combination ◽  
Repeated Game ◽  
Theoretic Approach ◽  
Worst Case ◽  
Point Distribution ◽  
Demand Distribution ◽  
Deterministic Solution ◽  
Uncertainty Set ◽  
Game Theoretic

This paper studies the Newsvendor problem for a setting in which (i) the demand is temporally correlated, (ii) the demand is censored, (iii) the distribution of the demand is unknown. The correlation is modeled as a Markovian process. The censoring means that if the demand is larger than the action (selected inventory), only a lower bound on the demand can be revealed. The uncertainty set on the demand distribution is given by only the upper and lower bound on the amount of the change from a time to the next time. We propose a robust approach to minimize the worst-case total cost and model it as a min-max zero-sum repeated game. We prove that the worst-case distribution of the adversary at each time is a two-point distribution with non-zero probabilities at the extrema of the uncertainty set of the demand. And the optimal action of the decision-maker can have any of the following structures: (i) a randomized solution with a two-point distribution at the extrema, (ii) a deterministic solution at a convex combination of the extrema. Both above solutions balance over-utilization and under-utilization costs. Finally, we extend our results to uni-model cost functions and present numerical results to study the solution.

Survey on aflatoxin in beer sold in Spain and other European countries

2013 ◽  
Vol 6 (1) ◽  
pp. 93-101 ◽  
Author(s):  
P.A. Burdaspal ◽  
T.M. Legarda
Keyword(s):  
Liquid Chromatography ◽  
Lower Bound ◽  
Fluorescence Detection ◽  
Analytical Procedure ◽  
European Countries ◽  
Retail Market ◽  
Case Scenario ◽  
Worst Case ◽  
The Mean ◽  
Per Capita

Aflatoxins (B1, B2, G1 and G2) were surveyed in 417 beer samples purchased from the retail market in Spain (n=336), France (n=49), Portugal (n=15), Ireland (n=11) and Italy (n=6) in the period 2006-2012. In addition, 4 samples were acquired from Ghana and one from Israel. The analytical procedure was based on immunoaffinity clean-up and liquid chromatography with fluorescence detection. Aflatoxin was detected in 72.6% of the samples acquired in the Spanish market and in 182 out of 200 samples brewed in Spain with levels ranging from 0.08 to 36.12 ng/l for all four aflatoxins. The mean and median values of positive samples were estimated to be 3.51 and 2.07 ng/l, respectively, for samples acquired in Spain and 3.82 and 2.60 ng/l, respectively, for samples brewed in Spain. The mean and median values for the group of imported beers were 2.64 and 0.51 ng/l, respectively. Regarding the whole group of beers from European countries (417 samples), the incidence of positive samples was 64.7% with concentrations ranging from 0.07 to 45.18 ng/l for total aflatoxins with mean and median values of 3.47 and 1.82 ng/l, respectively. The overall median concentrations of aflatoxins in the samples of beers produced in Spain were 2.27-2.32 ng/l and for the whole group of European beers 0.43-0.62 ng/l (lower bound - upper bound). The median values obtained in this study for aflatoxin in beers consumed in Spain would result in an intake of approx. 97-112 pg/per capita/day, which represents a very small fraction (approx. 0.5% in a worst-case scenario) of the estimated average exposure to total aflatoxins.

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