An Efficient Algorithm for Finding Similar Short Substrings from
... For the problem of finding substrings of S with the shortest Hamming distance to Q, Abrahamson[1] proposed an algorithm running in O(|S|(|Q| log |Q|)1/2 ) time. If the maximum Hamming distance is k, the computation time can be reduced to O(|S|(k log k)1/2 )[4]. Some approximation approaches have been ...
... For the problem of finding substrings of S with the shortest Hamming distance to Q, Abrahamson[1] proposed an algorithm running in O(|S|(|Q| log |Q|)1/2 ) time. If the maximum Hamming distance is k, the computation time can be reduced to O(|S|(k log k)1/2 )[4]. Some approximation approaches have been ...
Problem Set 2 Solutions - Massachusetts Institute of Technology
... because of other elements being missorted. Similarly, some elements may appear entirely out of place, but be good because of other misplaced elements. A key element of the proof is showing that a badly sorted list has a lot of bad elements. Lemma 5 If the list A is not 90% sorted, then at least 10% ...
... because of other elements being missorted. Similarly, some elements may appear entirely out of place, but be good because of other misplaced elements. A key element of the proof is showing that a badly sorted list has a lot of bad elements. Lemma 5 If the list A is not 90% sorted, then at least 10% ...
Variations of Diffie
... given a triple (g, gx, gz), where gz is either of the form gy or g x2 choose two strings s, t at random, compute u←(gx)s, v←(gx)t, w←(gz)st if (g, gx, gz) is square DH triple, then (g, u, v, w) is a DH quadruple input (g, u, v, w) to the distinguisher D to obtain correct value b ∈ {0,1} ...
... given a triple (g, gx, gz), where gz is either of the form gy or g x2 choose two strings s, t at random, compute u←(gx)s, v←(gx)t, w←(gz)st if (g, gx, gz) is square DH triple, then (g, u, v, w) is a DH quadruple input (g, u, v, w) to the distinguisher D to obtain correct value b ∈ {0,1} ...
4 per page - esslli 2016
... designing/finding an algorithm A that solves P, showing that A is sound, complete, and terminating showing that A runs, for every m ∈ M, in at most C ressources ...
... designing/finding an algorithm A that solves P, showing that A is sound, complete, and terminating showing that A runs, for every m ∈ M, in at most C ressources ...
Range-Efficient Counting of Distinct Elements in a Massive Data
... space linear in the input size. Thus, we focus on designing randomized approximation schemes for range-efficient computation of F0 . Definition 1. For parameters 0 < < 1 and 0 < δ < 1, an (, δ)-estimator for a number Y is a random variable X such that Pr[|X − Y | > Y ] < δ. 1.1. Our results. We co ...
... space linear in the input size. Thus, we focus on designing randomized approximation schemes for range-efficient computation of F0 . Definition 1. For parameters 0 < < 1 and 0 < δ < 1, an (, δ)-estimator for a number Y is a random variable X such that Pr[|X − Y | > Y ] < δ. 1.1. Our results. We co ...
Document
... • Step 1: If the problem size is small, solve this problem directly; otherwise, split the original problem into 2 sub-problems with equal sizes. • Step 2: Recursively solve these 2 sub-problems by applying this algorithm. • Step 3: Merge the solutions of the 2 sub-problems into a solution of the ori ...
... • Step 1: If the problem size is small, solve this problem directly; otherwise, split the original problem into 2 sub-problems with equal sizes. • Step 2: Recursively solve these 2 sub-problems by applying this algorithm. • Step 3: Merge the solutions of the 2 sub-problems into a solution of the ori ...
Efficient quantum algorithms for some instances of the non
... A nice representation of a factor Gi /Gi+1 means a homomorphism from Gi with kernel Gi+1 to either a permutation group of degree polynomially bounded in the input size + ν(G) or to Zp where p is a prime dividing |G|. Of course, if G is solvable one can insist that the representations of all the cycl ...
... A nice representation of a factor Gi /Gi+1 means a homomorphism from Gi with kernel Gi+1 to either a permutation group of degree polynomially bounded in the input size + ν(G) or to Zp where p is a prime dividing |G|. Of course, if G is solvable one can insist that the representations of all the cycl ...
A+B
... • Intractable: The situation is much worse for problems that cannot be solved using an algorithm with worst-case polynomial time complexity. The problems are called intractable. • NP problem. • NP-complete problem. • Unsolvable problem: no algorithm to solve them. ...
... • Intractable: The situation is much worse for problems that cannot be solved using an algorithm with worst-case polynomial time complexity. The problems are called intractable. • NP problem. • NP-complete problem. • Unsolvable problem: no algorithm to solve them. ...
Parallel Prefix
... in parallel: we can just break the array recursively into two halves, and add the sums of the two halves, recursively. Associated with the computation is a complete binary tree, each internal node containing the sum of its descendent leaves. With n processors, this algorithm takes O(log n) steps. If ...
... in parallel: we can just break the array recursively into two halves, and add the sums of the two halves, recursively. Associated with the computation is a complete binary tree, each internal node containing the sum of its descendent leaves. With n processors, this algorithm takes O(log n) steps. If ...
CS 391L: Machine Learning: Computational
... • An unbiased hypothesis space shatters the entire instance space. • The larger the subset of X that can be shattered, the more expressive the hypothesis space is, i.e. the less biased. • The Vapnik-Chervonenkis dimension, VC(H). of hypothesis space H defined over instance space X is the size of the ...
... • An unbiased hypothesis space shatters the entire instance space. • The larger the subset of X that can be shattered, the more expressive the hypothesis space is, i.e. the less biased. • The Vapnik-Chervonenkis dimension, VC(H). of hypothesis space H defined over instance space X is the size of the ...
here
... enabling them to make decisions without human intervention. Full autonomy has two clear benefits over pre-programming and human remote control. First, in contrast to sensors with pre-programmed motion paths, autonomous sensors are better able to adapt to their environment, and react to a priori unkn ...
... enabling them to make decisions without human intervention. Full autonomy has two clear benefits over pre-programming and human remote control. First, in contrast to sensors with pre-programmed motion paths, autonomous sensors are better able to adapt to their environment, and react to a priori unkn ...
Document
... • We ran the algorithm 300 times on a Sun Ultra 60. • The max iteration number was 1000 (if FC part does not have solutions, it randomly re-execute MC part). • We recorded every k value from 0 through n with an interval of 2. • An output parameter ‘Label count’ is the number of label that the algori ...
... • We ran the algorithm 300 times on a Sun Ultra 60. • The max iteration number was 1000 (if FC part does not have solutions, it randomly re-execute MC part). • We recorded every k value from 0 through n with an interval of 2. • An output parameter ‘Label count’ is the number of label that the algori ...
ALG3.2
... Fourier Transform is Polynomial Evaluation at the Roots of Unity Input a column n-vector a = (a0, …, an-1)T Output an n-vector (f0, …, fn-1)T which are the values polynomial f(x)at the n roots of unity ...
... Fourier Transform is Polynomial Evaluation at the Roots of Unity Input a column n-vector a = (a0, …, an-1)T Output an n-vector (f0, …, fn-1)T which are the values polynomial f(x)at the n roots of unity ...
Routing
... ◦ Claim 2. Dj is, for each j, the shortest distance between j and 1, using paths whose nodes all belong to P (except, possibly, j) • Given the above two properties ◦ When algorithm stops, the shortest path lengths must be equal to Dj , for all j → That is, algorithm finds the shortest path as desire ...
... ◦ Claim 2. Dj is, for each j, the shortest distance between j and 1, using paths whose nodes all belong to P (except, possibly, j) • Given the above two properties ◦ When algorithm stops, the shortest path lengths must be equal to Dj , for all j → That is, algorithm finds the shortest path as desire ...
An Algorithm For Finding the Optimal Embedding of
... 3.2.1. The Active-Set Method. The primal active-set method finds solutions of convex quadratic programming problems with linear equality and inequality constraints by iteratively solving a convex quadratic subproblem with only equality constraints. These constraints include all equality constraints ...
... 3.2.1. The Active-Set Method. The primal active-set method finds solutions of convex quadratic programming problems with linear equality and inequality constraints by iteratively solving a convex quadratic subproblem with only equality constraints. These constraints include all equality constraints ...
