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Polynomial Delay
In the analysis of algorithms, an enumeration algorithm (i.e., an algorithm for listing a large or infinite collection of structures) is said to have polynomial delay if the time between the output of any one structure and the next is bounded by a polynomial function of the input size, in the worst case. Polynomial delay implies that the total time used by an algorithm will be polynomial per output item, but is a stronger requirement. This is a desirable property, because it means that any consumer of the stream of outputs will not have to wait idle for a long time from one output to the next. In particular, an algorithm with polynomial delay cannot have a startup phase that takes exponential time before it produces a single output, unlike some algorithms that take polynomial time per output item.. Additionally, unlike bounds on the total time, it is a suitable form of analysis even for algorithms that produce an infinite sequence of outputs. The notion of polynomial delay was fir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analysis Of Algorithms
In computer science, the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to execute them. Usually, this involves determining a function that relates the size of an algorithm's input to the number of steps it takes (its time complexity) or the number of storage locations it uses (its space complexity). An algorithm is said to be efficient when this function's values are small, or grow slowly compared to a growth in the size of the input. Different inputs of the same size may cause the algorithm to have different behavior, so best, worst and average case descriptions might all be of practical interest. When not otherwise specified, the function describing the performance of an algorithm is usually an upper bound, determined from the worst case inputs to the algorithm. The term "analysis of algorithms" was coined by Donald Knuth. Algorithm analysis is an important part of a broader ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enumeration Algorithm
In computer science, an enumeration algorithm is an algorithm that enumerates the answers to a computational problem. Formally, such an algorithm applies to problems that take an input and produce a list of solutions, similarly to function problems. For each input, the enumeration algorithm must produce the list of all solutions, without duplicates, and then halt. The performance of an enumeration algorithm is measured in terms of the time required to produce the solutions, either in terms of the total time required to produce all solutions, or in terms of the maximal delay between two consecutive solutions and in terms of a preprocessing time, counted as the time before outputting the first solution. This complexity can be expressed in terms of the size of the input, the size of each individual output, or the total size of the set of all outputs, similarly to what is done with output-sensitive algorithms. Formal definitions An enumeration problem P is defined as a relation R ov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Worst Case
In computer science, best, worst, and average cases of a given algorithm express what the resource usage is ''at least'', ''at most'' and ''on average'', respectively. Usually the resource being considered is running time, i.e. time complexity, but could also be memory or some other resource. Best case is the function which performs the minimum number of steps on input data of n elements. Worst case is the function which performs the maximum number of steps on input data of size n. Average case is the function which performs an average number of steps on input data of n elements. In real-time computing, the worst-case execution time is often of particular concern since it is important to know how much time might be needed ''in the worst case'' to guarantee that the algorithm will always finish on time. Average performance and worst-case performance are the most used in algorithm analysis. Less widely found is best-case performance, but it does have uses: for example, where the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Time
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally expresse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David S
David (; , "beloved one") (traditional spelling), , ''Dāwūd''; grc-koi, Δαυΐδ, Dauíd; la, Davidus, David; gez , ዳዊት, ''Dawit''; xcl, Դաւիթ, ''Dawitʿ''; cu, Давíдъ, ''Davidŭ''; possibly meaning "beloved one". was, according to the Hebrew Bible, the third king of the United Kingdom of Israel. In the Books of Samuel, he is described as a young shepherd and harpist who gains fame by slaying Goliath, a champion of the Philistines, in southern Canaan. David becomes a favourite of Saul, the first king of Israel; he also forges a notably close friendship with Jonathan, a son of Saul. However, under the paranoia that David is seeking to usurp the throne, Saul attempts to kill David, forcing the latter to go into hiding and effectively operate as a fugitive for several years. After Saul and Jonathan are both killed in battle against the Philistines, a 30-year-old David is anointed king over all of Israel and Judah. Following his rise to power, David ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mihalis Yannakakis
Mihalis Yannakakis ( el, Μιχάλης Γιαννακάκης; born 13 September 1953 in Athens, Greece)Columbia University: CV: Mihalis Yannakakis (accessed 12 November 2009) is professor of computer science at Columbia University. He is noted for his work in , databases, and other related fields. He won the Donald E. Knuth Prize in 2005. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christos Papadimitriou
Christos Charilaos Papadimitriou ( el, Χρήστος Χαρίλαος "Χρίστος" Παπαδημητρίου; born August 16, 1949) is a Greek theoretical computer scientist and the Donovan Family Professor of Computer Science at Columbia University. Education Papadimitriou studied at the National Technical University of Athens, where in 1972 he received his Bachelor of Arts degree in electrical engineering. He then pursued graduate studies at Princeton University, where he received his Ph.D. in electrical engineering and computer science in 1976 after completing a doctoral dissertation titled "The complexity of combinatorial optimization problems." Career Papadimitriou has taught at Harvard, MIT, the National Technical University of Athens, Stanford, UCSD, University of California, Berkeley and is currently the Donovan Family Professor of Computer Science at Columbia University. Papadimitriou co-authored a paper on pancake sorting with Bill Gates, then a Harvard undergra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
