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Filtering Algorithms for Discrete Cumulative Resources, Abstract

→ Abstract
1 Introduction
2-3 Theory/Implementation, Experimental Results
6 Conclusion

Abstract

Edge finding is an algorithm commonly used in constraint-based scheduling. For problems of n tasks, several O(n log(n)) algorithms exist for edge finding in unary resource scheduling; however , edge finding with cumulative resources is more complicated, resulting in O(kn2) complexity at best (where k is the number of distinct resource demands). Recently Vilím [40] proposed a new algorithm for cumulative edge finding, which uses a novel data structure called the theta tree to improve the complexity to O(kn log(n)). This thesis presents work performed while implementing this new algorithm . Several areas not covered in the original paper, such as the choice of tree structure and best loop order in the adjustment phase, are discussed here. Additionally , several minor improvements to the algorithm are described, and two significant errors in the original paper identified. The symmetry of adjusting each task’s upper and lower bounds is considered in detail, and a proof of the monotonicity of the algorithm is provided. Also, issues in creating a parallel version of this algorithm are discussed , and implementation details for several parallel version are provided . In a separate paper , Vilím used the theta tree to design a max energy filtering algorithm, which handles tasks with variable durations and resource demands; this algorithm is also implemented here, and combined with the edge-finding algorithm.

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Subjects: Computer science
Text types: Master thesis

Abstract

Research papers like articles, theses, and lab reports almost always require an Abstract, which can be thought of as a special type of summary. The Abstract is the first section of such texts (usually no more than 1–2 paragraphs and/or 150–300 words long), and it should summarize the purpose of the study, its method and/or theoretical approach, and its main findings. The Abstract is an independent text that a reader should be able to understand without reading the longer text that it summarizes.

When writing an Abstract, make sure to provide a clear and accurate picture of your study so that the reader can decide whether or not the paper is relevant for her purposes. Remember that the Abstract is in many cases the only part of your text that will be read.

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Adverbial placement

Varying where in the sentence an adverbial is placed is an effective way of making the sentence structure less repetitive, thus making the text more interesting to read. Here, the adverbial can be found at the beginning of the sentence, rather than towards the end. By placing it at the beginning of the sentence, the author makes the topic/setting of the sentence clear from the start, which is helpful for the reader.

In the present study, socioeconomic status did not appear to confound the results.

Compare:

Socioeconomic status did not appear to confound the results in the present study.

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Using am / is / was

Am, is, and was are used with singular subjects. Am is the 1st person present tense; is is the 3rd person present tense; was is the 1st and 3rd-person past tense.

Present: (1st person) I am late. (3rd person) She is late. He is late. It is gone.

Past: (1st person) I was late. (3rd person) She was late. He was late. It was gone.

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Choosing the right relative pronoun

Relative pronouns are words like that and which, and they are used to replace a word or phrase in a previous phrase or sentence. Using relative pronouns correctly increases clarity, and makes a text more formal. It is important to note that that the use of these words in writing may differ slightly from their use in spoken English.

ESL Tips on the Use of Relative Pronouns

[Source: https://owl.english.purdue.edu/owl/resource/645/03/]

Although there is no one single rule to cover all the cases, the following summary may be helpful if you need to make a quick decision:

Use that if the main clause poses the question WHAT? answered by the relative clause;
Do not use that presenting non-essential, additional information (that is, in non-defining relative clauses); use who or which instead;
Use who to refer to people;
Use which to refer to things or to refer to the previous clause as a whole;
If you choose between who or that, use who in writing;
If you choose between which and that, use which in writing;
Do not put a comma before that.

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Demonstrative pronouns

The common demonstrative pronouns are this and that (singular) and these and those (plural). These words are used to take the place of an entire phrase. Demonstrative pronouns should only be used when the meaning is unambiguous.

Constraint programming is a declarative programming method for modeling combinatorial optimization problems in terms of constraints. This is a fairly dense statement, so let us address the concepts one at a time.

Runic artefacts are both textual sources and archaeological artefacts. Because of this it will be important to classify runic artefacts according to both function and inscription.

[Generally, it is a good idea to avoid using too many demonstrative pronouns. An alternative is to use a demonstrative adjective, as this form is often more clear.]

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Demonstrative adjectives

The demonstrative adjectives are this, that, these, and those, and they are used to emphasize exactly which thing is being referred to. (These words can also be used as pronouns.)

This study will use non-monumental artefacts that bear runic inscriptions. These inscriptions do not necessarily follow the same formulas as displayed on rune stones.

Further research showed those earlier conclusions to be misleading.

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however

The transition word however signals to the reader that what is to follow is a contrast or exception to what has been said just before in the text.

The magnetic energy was increased by changing the pole shoes. However, there is an upper limit to how high the magnetic field in the stator steel should be to work at its best.

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Using is / are

Whether to use is or are depends on whether the subject of the sentence is single or plural. The choice can be confusing when the subject and the noun closest to the verb are not in the same number, as in the following examples.

This category of puzzles is very challenging for humans. (subject is singular, “This category”)

Puzzles falling into this category are very challenging for humans. (subject is plural, “Puzzles”)

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moreover / furthermore / in addition / additionally

The words moreover, in addition, additionally, and furthermore can be used as transition words to indicate that additional information will be presented.

Short range weather forecasts can predict where a storm will happen, but longer range forecasts often cannot. Moreover/Additionally/In addition, calculating even a short range forecast can be very computationally intensive. Furthermore, even if a pilot had a powerful computer, it would still be impossible to forecast the exact timing and location of a lightening strike.

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Numbered (Vancouver) citation style

The Numbered, or Vancouver, style of referencing is commonly used in sciences and engineering. Numbered bibliographies are created according to one of two styles (see below), and the works are then cited in the text according to these numbers. The numbers are usually enclosed in parentheses or square brackets.

Style 1: Works are listed in the bibliograpy alphabetically according to the order of the first author’s last name, and are numbered consecutively; those numbers are then used persistantly for in-text citations. (The numbers will not be consecutive in the running text.)

Style 2: Works are listed in the bibliography according to the order in which they are cited in the text; those numbers are then used persistantly for in-text citations. (The numbers will be consecutive in the running text.)

In-text citations will look something like this:

Edge-finding was first applied to scheduling problems in [2], and since that time several efficient algorithms have been developed for the disjunctive case [10, 41].

The reference list (here made in Style 1) will look something like this:

[1] Abderrahmane Aggoun and Nicolas Beldiceanu. Extending CHIP in order to solve complex scheduling and placement problems. Mathematical and Computer Modelling, 17(7):57–73, 1993.

[2] David Applegate and William Cook. A computational study of the job-shop scheduling problem. INFORMS Journal on Computing, 3(2):149–156, 1991.

…

[10] Jacques Carlier and Eric Pinson. Adjustment of heads and tails for the jobshop problem. European Journal of Operational Research, 78(2):146–161, 1994.

…

[41] Petr Vilím, Roman Bartak, and Ondrej Cepek. Unary resource constraint with optional activities. In Principles and Practice of Constraint Programming, volume 3258 of Lecture Notes in Computer Science, pages 62–76. Springer, 2004.

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Singular possessive

The singular possessive is formed by adding an apostrophe-s (’s) to the end of the word.

The player’s experience is analysed using a new technique.

The form is the same when a single subject possesses more than one thing.

A smith’s tools were considered masculine, while a weaver’s tools were attributed to the feminine gender.

Collective nouns, such as “people” or “team”, still take the singular possessive form when the noun is treated as a single entity.

The team’s positive attitude could be seen in its cheerful training session.

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Using the passive voice

The passive voice is often used when describing methodology. Using the passive voice emphasizes the action taken rather than the entity performing the action. In each of the following examples, the author or authors are the (unspecified) actors.

The specimens were collected according to established protocols. (instead of “I collected specimens…”)

Several factors have been taken into consideration before categorizing artefacts. (instead of “I took several factors into consideration…”)

The questions for the interviews were formed using our theoretical framework. (instead of “We formed the questions…”)

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Using the s-ending for verbs

With a third-person singular subject, the verb takes an –s in the present tense. That is, when the subject is 1) only a single entity that could be replaced by “she,” “he” or “it” and 2) the action takes place in the present, one adds the letter s to the verb.

This new computer runs faster than the old one. It saves time.

Compare to the following sentence with plural subjects, in which the present tense does not take the s ending.

These new computers run faster than the old ones. They save time.

If the main verb is separated from the subject by many words, it can be tricky to pick out which word is the subject. In the following, the subject is “Problems” (plural) and the main verb is “fall” (to agree with the plural subject).

Problems for which there exists a solution algorithm that completes in a time that grows in a polynomial fashion with the problem size fall into the set P.

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Using where

The relative pronoun where is used when a physical location is being referred to. Where is also often used when identifying variables in equations or in figures.

The lab where the element was discovered burned down in 1902.

The relationship between the displacement field, the electric field and the polarization is D = ε0E + P, where ε0 is the electric constant.

Where can also be used to refer to publications, although the phrase “in which” is more formal than where in these cases.

Arwill-Nordbladh wrote a compendium of gender theory in archaeology, where she argues that archaeology is androcentric in numerous ways.

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Using which

The relative pronouns which and that are easily confused, and there is no definitive correct usage; furthermore, these words are often used differently in speech. However, the two words are generally not used in an exactly identical fashion in writing. Which often refers to the idea presented by the entire previous clause, and the word is commonly used to introduce non-restrictive clauses (see below).

A claim was made that the pendant belongs to a “female hoard”, which is one of the claims examined in this thesis.

The phrase “which is one of the claims examined in this thesis” is called a non-restrictive or non-defining clause, because this clause does not add crucial information to the main clause. This type of clause is (usually) set off by a comma.

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Texts, Tools, and Tips for Academic Writing

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Filtering Algorithms for Discrete Cumulative Resources, Abstract

Abstract

Abstract

Adverbial placement

Using am / is / was

Choosing the right relative pronoun

ESL Tips on the Use of Relative Pronouns

Demonstrative pronouns

Demonstrative adjectives

however

Using is / are

moreover / furthermore / in addition / additionally

Numbered (Vancouver) citation style

Singular possessive

Using the passive voice

Using the s-ending for verbs

Using where

Using which