منابع مشابه
On finding an ear decomposition of an undirected graph distributively
An ear decomposition of a connected undirected graph G= (V ,E) is a partition of the edge (link) set E into a collection of edge-disjoint paths P0,P1, . . . ,P|E|−|V |+1, called ears, such that P0 is a link, P0 ∪P1 is a closed path (i.e., a cycle), and for each i , 2 i |E| − |V | + 1, Pi is a path of which each terminating node belongs to some Pj , j < i , and no internal node belongs to any Pj...
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We explain the ingredients of the International Olympiad in Informatics (IOI), which is a challenging competition for high-school students focusing on algorithmic problem solving. We treat in detail the MEDIAN task, which the authors created for IOI 2000: Given an odd number of objects, all of distinct strength, develop an efficient algorithm to determine the object of median strength, using as...
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For some computational problems (like sorting), even though the input is given and known (deterministic), it might be helpful to use randomness (probabilitic processes) in the design of the algorithm. This is analogous to the probabilistic method in which we were using probability to prove the existence of a certain object. We’ll see several examples of randomized algorithms in this course, one...
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We prove that any oblivious algorithm using space S to find the median of a list of n integers from {1, . . . , 2n} requires time Ω(n log logS n). This bound also applies to the problem of determining whether the median is odd or even. It is nearly optimal since Chan, following Munro and Raman, has shown that there is a (randomized) selection algorithm using only s registers, each of which can ...
متن کاملAnalyzing Randomized Median Finding and Quicksort
In a previous lecture, we discussed the problem of finding the median of a list of m elements, or more generally the element of rank m. The approach we followed was to select a pivot element p, to compute its rank, and partition the list into 2 sublists, one containing the elements smaller than p, the other containing those larger than p. By comparing m, the desired rank, to the size of these l...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 1982
ISSN: 0022-0000
DOI: 10.1016/0022-0000(82)90045-9