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Online Algorithm
In computer science, an online algorithm is one that can process its input piece-by-piece in a serial fashion, i.e., in the order that the input is fed to the algorithm, without having the entire input available from the start. In contrast, an offline algorithm is given the whole problem data from the beginning and is required to output an answer which solves the problem at hand. In operations research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and ..., the area in which online algorithms are developed is called online optimization. As an example, consider the sorting algorithms selection sort and insertion sort: selection sort repeatedly selects the minimum element from the unsorted remainder and places it at the front, which requires access to the entire input; it is thus a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Odds Algorithm
In decision theory, the odds algorithm (or Bruss algorithm) is a mathematical method for computing optimal strategies for a class of problems that belong to the domain of optimal stopping problems. Their solution follows from the ''odds strategy'', and the importance of the odds strategy lies in its optimality, as explained below. The odds algorithm applies to a class of problems called ''last-success'' problems. Formally, the objective in these problems is to maximize the probability of identifying in a sequence of sequentially observed independent events the last event satisfying a specific criterion (a "specific event"). This identification must be done at the time of observation. No revisiting of preceding observations is permitted. Usually, a specific event is defined by the decision maker as an event that is of true interest in the view of "stopping" to take a well-defined action. Such problems are encountered in several situations. Examples Two different situations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ski Rental Problem
In computer science, the ski rental problem is a name given to a class of problems in which there is a choice between continuing to pay a repeating cost or paying a one-time cost which eliminates or reduces the repeating cost. The problem Many online problems have a sub-problem called the rent-or-buy problem. Given an expensive up front cost, or a less expensive repeating cost, with no knowledge of how the future will play out, at what point is it better to pay the up front cost to avoid a continued repeating cost? Consider a person who decides to go skiing, but for an undecided number of days. Renting skis costs $1 per day, whereas buying a pair of skis costs $10. If the person knows in advance how many days they want to ski, then the breakeven point is 10 days. Fewer than 10 days, renting is preferable, whereas with more than 10 days, buying is preferable. However, with no advance knowledge of how long one will be skiing, the breakeven point is unclear. A good algorithm will m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Search Games
A search game is a two-person zero-sum game which takes place in a set called the search space. The searcher can choose any continuous trajectory subject to a maximal velocity constraint. It is always assumed that neither the searcher nor the hider has any knowledge about the movement of the other player until their distance apart is less than or equal to the discovery radius and at this very moment capture occurs. The game is zero sum with the payoff being the time spent in searching. As mathematical models, search games can be applied to areas such as hide-and-seek games that children play or representations of some tactical military situations. The area of search games was introduced in the last chapter of Rufus Isaacs' classic book "Differential Games" and has been developed further by Shmuel GalS. Gal, ''Search Games'', Academic Press, New York (1980)S. Alpern and S. Gal, The Theory of Search Games and Rendezvous', Springer (2003). and Steve Alpern. The princess and monster ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Secretary Problem
The secretary problem demonstrates a scenario involving optimal stopping theory For French translation, secover storyin the July issue of ''Pour la Science'' (2009). that is studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem. Its solution is also known as the 37% rule. The basic form of the problem is the following: imagine an administrator who wants to hire the best secretary out of n rankable applicants for a position. The applicants are interviewed one by one in random order. A decision about each particular applicant is to be made immediately after the interview. Once rejected, an applicant cannot be recalled. During the interview, the administrator gains information sufficient to rank the applicant among all applicants interviewed so far, but is unaware of the quality of yet unseen applicants. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bandit Problem
Banditry is a type of organized crime committed by outlaws typically involving the threat or use of violence. A person who engages in banditry is known as a bandit and primarily commits crimes such as extortion, robbery, kidnapping, and murder, either as an individual or in groups. Banditry is a vague concept of criminality and in modern usage can be synonymous with gangsterism, brigandage, marauding, terrorism, piracy, and thievery. Definitions The term ''bandit'' (introduced to English via Italian around 1776) originates with the early Germanic legal practice of outlawing criminals, termed ''*bamnan'' (English ban). The legal term in the Holy Roman Empire was ''Acht'' or '' Reichsacht'', translated as "Imperial ban". In modern Italian, the equivalent word "bandito" literally means banned or a banned person. The New English Dictionary on Historical Principles (NED) defined "bandit" in 1885 as "one who is proscribed or outlawed; hence, a lawless desperate marauder, a brigand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Update Problem
The List Update or the List Access problem is a simple model used in the study of competitive analysis of online algorithms. Given a set of items in a list where the cost of accessing an item is proportional to its distance from the head of the list, e.g. a linked List, and a request sequence of accesses, the problem is to come up with a strategy of reordering the list so that the total cost of accesses is minimized. The reordering can be done at any time but incurs a cost. The standard model includes two reordering actions: * A free transposition of the item being accessed anywhere ahead of its current position; * A paid transposition of a unit cost for exchanging any two adjacent items in the list. Performance of algorithms depend on the construction of request sequences by adversaries under various adversary models An online algorithm for this problem has to reorder the elements and serve requests based only on the knowledge of previously requested items and hence its strategy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Job Shop Scheduling
Job-shop scheduling, the job-shop problem (JSP) or job-shop scheduling problem (JSSP) is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. In a general job scheduling problem, we are given ''n'' jobs ''J''1, ''J''2, ..., ''Jn'' of varying processing times, which need to be scheduled on ''m'' machines with varying processing power, while trying to minimize the makespan – the total length of the schedule (that is, when all the jobs have finished processing). In the specific variant known as ''job-shop scheduling'', each job consists of a set of ''operations'' ''O''1, ''O''2, ..., ''On'' which need to be processed in a specific order (known as ''precedence constraints''). Each operation has a ''specific machine'' that it needs to be processed on and only one operation in a job can be processed at a given time. A common relaxation is the flexible job shop, where each operation can be processed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-server Problem
The -server problem is a problem of theoretical computer science in the category of online algorithms, one of two abstract problems on metric spaces that are central to the theory of competitive analysis (the other being metrical task systems). In this problem, an online algorithm must control the movement of a set of ''k'' ''servers'', represented as points in a metric space, and handle ''requests'' that are also in the form of points in the space. As each request arrives, the algorithm must determine which server to move to the requested point. The goal of the algorithm is to keep the total distance all servers move small, relative to the total distance the servers could have moved by an optimal adversary who knows in advance the entire sequence of requests. The problem was first posed by Mark Manasse, Lyle A. McGeoch and Daniel Sleator (1988). The most prominent open question concerning the ''k''-server problem is the so-called ''k''-server conjecture, also posed by Manasse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PSPACE-complete
In computational complexity theory, a decision problem is PSPACE-complete if it can be solved using an amount of memory that is polynomial in the input length (PSPACE, polynomial space) and if every other problem that can be solved in polynomial space can be Polynomial-time reduction, transformed to it in polynomial time. The problems that are PSPACE-complete can be thought of as the hardest problems in PSPACE, the class of decision problems solvable in polynomial space, because a solution to any one such problem could easily be used to solve any other problem in PSPACE. Problems known to be PSPACE-complete include determining properties of regular expressions and context-sensitive grammars, determining the truth of quantified Boolean formula problem, quantified Boolean formulas, step-by-step changes between solutions of combinatorial optimization problems, and many puzzles and games. Theory A problem is defined to be PSPACE-complete if it can be solved using a polynomial amount o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shortest Path Problem
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs, where the vertices correspond to intersections and the edges correspond to road segments, each weighted by the length or distance of each segment. Definition The shortest path problem can be defined for graphs whether undirected, directed, or mixed. The definition for undirected graphs states that every edge can be traversed in either direction. Directed graphs require that consecutive vertices be connected by an appropriate directed edge. Two vertices are adjacent when they are both incident to a common edge. A path in an undirected graph is a sequence of vertices P = ( v_1, v_2, \ldots, v_n ) \in V \times V \times \cdots \times V ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canadian Traveller Problem
In computer science and graph theory, the Canadian traveller problem (CTP) is a generalization of the shortest path problem to graphs that are partially observable. In other words, a "traveller" on a given point on the graph cannot see the full graph, rather only adjacent nodes or a certain "realization restriction." This optimization problem was introduced by Christos Papadimitriou and Mihalis Yannakakis in 1989 and a number of variants of the problem have been studied since. The name supposedly originates from conversations of the authors who learned of a difficulty Canadian drivers had: traveling a network of cities with snowfall randomly blocking roads. The stochastic version, where each edge is associated with a probability of independently being in the graph, has been given considerable attention in operations research under the name "the Stochastic Shortest Path Problem with Recourse" (SSPPR). Problem description For a given instance, there are a number of possibiliti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
