scholarly journals Bamboo Garden Trimming Problem: Priority Schedulings

Algorithms ◽  
2019 ◽  
Vol 12 (4) ◽  
pp. 74 ◽  
Author(s):  
Mattia D’Emidio ◽  
Gabriele Di Stefano ◽  
Alfredo Navarra
Keyword(s):  
Lower Bound ◽  
Growth Rates ◽  
Experimental Evaluation ◽  
Daily Growth ◽  
Worst Case ◽  
Priority Scheduling ◽  
Preliminary Results ◽  
Entire Height ◽  
Close Relationship ◽  
Input Instance

The paper deals with the Bamboo Garden Trimming (BGT) problem introduced in [Gąsieniec et al., SOFSEM’17]. The problem is difficult to solved due to its close relationship to Pinwheel scheduling. The garden with n bamboos is an analogue of a system of n machines that have to be attended (e.g., serviced) with different frequencies. During each day, bamboo b i grows an extra height h i , for i = 1 , ⋯ , n and, on the conclusion of the day, at most one bamboo has its entire height cut.The goal is to design a perpetual schedule of cuts to keep the height of the tallest ever bamboo as low as possible. The contribution in this paper is twofold, and is both theoretical and experimental. In particular, the focus is on understanding what has been called priority schedulings, i.e., cutting strategies where priority is given to bamboos whose current height is above a threshold greater than or equal to H = ∑ i = 1 n h i . Value H represents the total daily growth of the system and it is known that one cannot keep bamboos in the garden below this threshold indefinitely. As the first result, it is proved that, for any distribution of integer growth rates h 1 , ⋯ , h n and any priority scheduling, the system stabilises in a fixed cycle of cuts. Then, the focus is on the so-called ReduceMax strategy, a greedy priority scheduling that each day cuts the tallest bamboo, regardless of the growth rates distribution. ReduceMax is known to provide a O ( log n ) -approximation, with respect to the lower bound H. One of the main results achieved is that, if ReduceMax stabilises in a round-robin type cycle, then it guarantees 2-approximation. Furthermore, preliminary results are provided relating the structure of the input instance, in terms of growth rates, and the behavior of ReduceMax when applied to such inputs. Finally, a conjecture that ReduceMax is 2-approximating for the BGT problem is claimed, hence an extended experimental evaluation was conducted to support the conjecture and to compare ReduceMax with other relevant scheduling algorithms. The obtained results show that ReduceMax : (i) provides 2-approximation in all considered inputs; and (ii) always outperforms other considered strategies, even those for which better worst case approximation guarantees have been proven.

Density, growth, and change in density of coho salmon and rainbow trout in three Lake Michigan tributaries

1983 ◽  
Vol 61 (5) ◽  
pp. 1120-1127 ◽  
Author(s):  
L. M. Carl
Keyword(s):  
Rainbow Trout ◽  
Growth Rates ◽  
Lake Michigan ◽  
Coho Salmon ◽  
Daily Growth ◽  
Salmon Fry ◽  
Daily Change ◽  
Early Fall ◽  
Growth And Change ◽  
Downstream Movement

Coho salmon spawning peaked in the late fall. Spawning densities ranged from fewer than 5 coho salmon per hectare up to 90 fish per hectare. Subyearling coho salmon densities ranged from 10 to 60 fish per 100 m2 in June and dropped to 5–20 fish by early fall. Coho salmon fry increased in length from 40 mm in early May, to over 120 mm by smolt out-migration in the following April. Coho salmon instantaneous daily change in density coefficients ranged from 0.004 to 0.019 and were dependent on initial coho density. Daily coho salmon growth rates ranged from 0.38 to 0.60 mm per day and were not dependent on initial coho salmon density. Downstream movement of rainbow trout fry began in May, and continued into July. In the spring 10–20 yearlings and one to five 2-year-olds per 100 m2 were present. Most fry emerged in June at a size of 25 mm and grew to 85 mm by fall. Daily growth rates varied from 0.23 to 0.45 mm per day for yearling rainbow trout and were not correlated with rainbow trout density.

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 Age, growth, and recruitment patterns of juvenile ladyfish (Elopssp) from the east coast of Florida (USA)

PeerJ ◽  
2015 ◽  
Vol 3 ◽  
pp. e1392
Author(s):  
Juan C. Levesque
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Age And Growth ◽  
Growth Equation ◽  
Length Frequency ◽  
Daily Growth ◽  
Exponential Regression ◽  
Absolute Growth ◽  
Specific Growth Rates ◽  
Size At Age

Ladyfish (Elopssp) are a common and economically valuable coastal nearshore species found along coastal beaches, bays, and estuaries of the southeastern United States, and subtropical and tropical regions worldwide. Previously, ladyfish were a substantial bycatch in Florida’s commercial fisheries, but changes in regulations significantly reduced commercial landings. Today, ladyfish are still taken in commercial fisheries in Florida, but many are also taken by recreational anglers. Life-history information and research interest in ladyfish is almost non-existent, especially information on age and growth. Thus, the overarching purpose of this study was to expand our understanding of ladyfish age and growth characteristics. The specific objectives were to describe, for the first time, age, growth, and recruitment patterns of juvenile ladyfish from the east coast of Florida (USA). In the Indian River Lagoon (IRL), annual monthly length-frequency distributions were confounded because a few small individuals recruited throughout the year; monthly length-frequency data generally demonstrated a cyclical pattern. The smallest were collected in September and the largest in May. Post-hoc analysis showed no significant difference in length between August and May, or among the other months. In Volusia County (VC), annual monthly length-frequency distribution demonstrated growth generally occurred from late-winter and spring to summer. The smallest ladyfish were collected in February and the largest in August. On average, the absolute growth rate in the IRL was 36.3 mm in 60 days or 0.605 mm day−1. Cohort-specific daily growth rates, elevations, and coincidentals were similar among sampling years. Cohort-specific growth rates ranged from 1.807 in 1993 to 1.811 mm day−1in 1994. Overall, growth was best (i.e., goodness of fit) described by exponential regression. On average, the absolute growth rate in VC was 28 mm in 150 days or 0.1866 mm day−1. Cohort-specific daily growth rates were significantly different among sampling years; however, the elevations and coincidentals were similar. Cohort-specific growth rates ranged from 1.741 in 1994 to 1.933 mm day−1in 1993. Mean ladyfish growth was best described by linear regression; however, natural growth was explained better by exponential regression. In the IRL, the corrected exponential growth equation yielded a size-at-age 1 of 156.0 mm SL, which corresponded to an estimated growth rate of 0.4356 mm day−1. In VC, the corrected exponential growth equation yielded a size-at-age 1 of 80 mm SL corresponding to an estimated growth rate of 0.2361 mm day−1.

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].

scholarly journals Observations on the increase in size at moulting in the lobster (Homarus vulgaris M.-Edw.)

1958 ◽  
Vol 37 (3) ◽  
pp. 603-606 ◽  
Author(s):  
H. J. Thomas
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Growth Increment ◽  
American Lobster ◽  
Limited Data ◽  
Preliminary Results ◽  
Home Department ◽  
The Individual ◽  
Marine Laboratory

A knowledge of growth rates is a pre-requisite in estimating the effect of fishing upon the available stocks. In Crustacea, where there is no known means of establishing accurately the age of the individual, the importance of measuring the growth rate is increased whilst its determination is made more difficult. In Homarus vulgaris some experiments were undertaken by Dannevig (1936), and Wilder (1953) gives considerable data for the American lobster. Results suggest that the growth increment is not uniform in all latitudes. Experiments to augment the limited data available for H. vulgaris and to establish the increase in size at moulting in local lobster stocks were therefore undertaken by the Marine Laboratory of the Scottish Home Department at Aberdeen. A statement of some preliminary results was given in Report on the Fisheries of Scotland (Lucas, 1957, p. 58).

In situ growth rate estimates of Southern Ocean krill, Thysanoessa macrura

2019 ◽  
Vol 31 (3) ◽  
pp. 116-122 ◽  
Author(s):  
Jake R. Wallis ◽  
Jessica E. Melvin ◽  
Robert King ◽  
So Kawaguchi
Keyword(s):  
Growth Rate ◽  
Southern Ocean ◽  
Growth Rates ◽  
Somatic Growth ◽  
Growth Patterns ◽  
Daily Growth ◽  
Thysanoessa Macrura ◽  
Growth Method ◽  
Repeated Sampling ◽  
The Antarctic

AbstractGrowth, which is intrinsically linked to environmental conditions including temperature and food availability are highly variable both temporally and spatially. Estimates of growth rates of the Southern Ocean euphausiid Thysanoessa macrura are currently restricted to limited studies which rely upon repeated sampling and length-frequency analysis to quantify growth rates. The instantaneous growth method (IGR) was used to measure the growth rate of T. macrura successfully in the southern Kerulen Plateau region during summer, providing the first IGR parameters for the Southern Ocean euphausiid species. Results of the four-day IGR incubation indicate a period of low somatic growth for adult T. macrura. Males had a longer intermoult period (IMP) (62 days) than females (42 days), but the sexes exhibited similar daily growth rates of 0.011 mm day−1 and 0.012 mm day−1 respectively. Juveniles exhibited the fastest growth, with an IMP of 13 days and daily growth rate of 0.055 mm day−1 indicating a prolonged growth season, similar to the Antarctic krill E. superba. Consequently, we highlight the usability of the IGR method and strongly encourage its use in developing a comprehensive understanding of spatial and seasonal growth patterns of T. macrura.

Influence of biomass and ocean climate on the growth of Pacific herring (Clupea pallasi) from the southwest coast of Vancouver Island

1997 ◽  
Vol 54 (12) ◽  
pp. 2782-2788 ◽  
Author(s):  
R W Tanasichuk
Keyword(s):  
Growth Rates ◽  
Growing Season ◽  
Vancouver Island ◽  
Pacific Herring ◽  
Daily Growth ◽  
Sea Temperature ◽  
Clupea Pallasi ◽  
Southwest Coast ◽  
Growth Increments ◽  
Adult Growth

I examined the growth of Pacific herring (Clupea pallasi) from the southwest coast of Vancouver Island using data for over 83 000 fish seined between 1975 and 1996. Size-at-age (length, total mass) of recruits (age 3) was negatively related to parental biomass. Length was also negatively related to sea temperature over the first growing season and positively related to salinity later in the third growing season. Prerecruit effects explained variations in mass and length for adult herring ages 4 and 5, respectively. Growth of adults was described as growth increments (growth rates). Seasonal growth in length for adults was assumed to be a linear function of time, and growth in mass an exponential function. Daily growth rates for length were negatively related to initial length. Instantaneous daily growth rates in mass were a negative function of initial mass, adult biomass, and sea temperature in August. Interannual variations in condition suggest that adults grow differently in mass than they do in length. I suggest that length is not synonymous with mass as a measure of adult growth. Consequently, it provides little, if any, information on surplus energy accumulation by adults and therefore adult fish contribution to stock productivity.

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