Computing and proving with pivots
نویسنده
چکیده
A simple idea used in many combinatorial algorithms is the idea of pivoting. Originally, it comes from the method proposed by Gauss in the 19th century for solving systems of linear equations. This method had been extended in 1947 by Dantzig for the famous simplex algorithm used for solving linear programs. From since, a pivoting algorithm is a method exploring subsets of a ground set and going from one subset σ to a new one σ′ by deleting an element inside σ and adding an element outside σ: σ′ = σ \ {v} ∪ {u}, with v ∈ σ and u / ∈ σ. This simple principle combined with other ideas appears to be quite powerful for many problems. This present paper is a survey on algorithms in operations research and discrete mathematics using pivots. We give also examples where this principle allows not only to compute but also to prove some theorems in a constructive way. A formalisation is described, mainly based on ideas by Michael J. Todd.
منابع مشابه
A new network simplex algorithm to reduce consecutive degenerate pivots and prevent stalling
It is well known that in operations research, degeneracy can cause a cycle in a network simplex algorithm which can be prevented by maintaining strong feasible bases in each pivot. Also, in a network consists of n arcs and m nodes, not considering any new conditions on the entering variable, the upper bound of consecutive degenerate pivots is equal $left( begin{array}{c} n...
متن کاملSelecting sprinkler packages for center pivots
Center pivots are the primary method of irrigation across the U.S. Great Plains. Center-pivot irrigation is also the fastest growing method of irrigation in the U.S. and around the world. Pivots have the potential to be very efficient and uniform if sprinkler devices are properly selected for local field conditions. New water application devices provide for selection that minimizes runoff and c...
متن کاملPivot Selection Techniques for Proximity Searching in Metric Spaces
With few exceptions, proximity search algorithms in metric spaces based on the use of pivots select them at random among the objects of the metric space. However, it is well known that the way in which the pivots are selected can drastically affect the performance of the algorithm. Between two sets of pivots of the same size, better chosen pivots can largely reduce the search time. Alternativel...
متن کاملUnsupervised Cross-Domain Word Representation Learning
Meaning of a word varies from one domain to another. Despite this important domain dependence in word semantics, existing word representation learning methods are bound to a single domain. Given a pair of source-target domains, we propose an unsupervised method for learning domain-specific word representations that accurately capture the domainspecific aspects of word semantics. First, we selec...
متن کاملLinking Heterogeneous Input Features with Pivots for Domain Adaptation
Sentiment classification aims to automatically predict sentiment polarity (e.g., positive or negative) of user generated sentiment data (e.g., reviews, blogs). In real applications, these user generated sentiment data can span so many different domains that it is difficult to manually label training data for all of them. Hence, this paper studies the problem of domain adaptation for sentiment c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- RAIRO - Operations Research
دوره 47 شماره
صفحات -
تاریخ انتشار 2013