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Pointsto Analysis in Almost Linear Time
, 1996
"... We present an interprocedural flowinsensitive pointsto analysis based on type inference methods with an almost linear time cost complexity. To our knowledge, this is the asymptotically fastest nontrivial interprocedural pointsto analysis algorithm yet described. The algorithm is based on a nons ..."
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Cited by 590 (3 self)
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We present an interprocedural flowinsensitive pointsto analysis based on type inference methods with an almost linear time cost complexity. To our knowledge, this is the asymptotically fastest nontrivial interprocedural pointsto analysis algorithm yet described. The algorithm is based on a non
Identifying Loops In Almost Linear Time
 ACM Transactions on Programming Languages and Systems
, 1999
"... this paper, we study and improve three recently proposed algorithms for identifying loops in an irreducible graph. The first algorithm we study is due to Havlak [1997]. We show that the running time of this algorithm is quadratic in the worstcase, and not almostlinear as claimed. We then show how ..."
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Cited by 20 (1 self)
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this paper, we study and improve three recently proposed algorithms for identifying loops in an irreducible graph. The first algorithm we study is due to Havlak [1997]. We show that the running time of this algorithm is quadratic in the worstcase, and not almostlinear as claimed. We then show how
Computing maximumscoring segments in almost linear time
 IN PROCEEDINGS OF THE 12TH ANNUAL INTERNATIONAL COMPUTING AND COMBINATORICS CONFERENCE, VOLUME 4112 OF LNCS
, 2006
"... Given a sequence, the problem studied in this paper is to find a set of k disjoint continuous subsequences such that the total sum of all elements in the set is maximized. This problem arises naturally in the analysis of DNA sequences. The previous best known algorithm requires Θ(n log n) time in th ..."
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Cited by 3 (1 self)
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in the worst case. For a given sequence of length n, we present an almost lineartime algorithm for this problem. Our algorithm uses a disjointset data structure and requires O(nα(n, n)) time in the worst case, where α(n, n) is the inverse Ackermann function.
An (almost) Linear Time Algorithm For Odd Cycles Transversal
, 2009
"... We consider the following problem, which is called the odd cycles transversal problem. Input: A graph G and an integer k. Output: A vertex set X ∈ V (G) with X  ≤ k such that G − X is bipartite. We present an O(mα(m, n)) time algorithm for this problem for any fixed k, where n, m are the number o ..."
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Cited by 11 (1 self)
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We consider the following problem, which is called the odd cycles transversal problem. Input: A graph G and an integer k. Output: A vertex set X ∈ V (G) with X  ≤ k such that G − X is bipartite. We present an O(mα(m, n)) time algorithm for this problem for any fixed k, where n, m are the number
2 Local and Almost LinearTime Clustering and Partitioning
, 2009
"... You should probably know that • the first problem set (due October 15) is posted on the class website, and • its hints are also posted there. Also, today in class there was a majority vote for posting problem sets earlier. Professor Kelner will post the problem sets from two years ago, but he reserv ..."
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reserves the right to add new problems once a problem set has already been posted. Questions from last time. • What is a level set? The level set of a function corresponding to a (fixed) constant c is the set of points in the function’s domain whose image equals c. • What is a good reference
Almost linear time operations with triangular sets
 ACM COMMUNICATIONS IN COMPUTER ALGEBRA, TBA
"... Let F be a perfect field, and let X = X1,..., Xn be indeterminates over F. A (monic) triangular set T = (T1,..., Tn) is a family of polynomials in F[X] such that for all i, Ti is in F[X1,..., Xi], monic in Xi, and reduced modulo 〈T1,..., Ti−1〉. The degree of T is the product deg(T1, X1) · · · deg ..."
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Let F be a perfect field, and let X = X1,..., Xn be indeterminates over F. A (monic) triangular set T = (T1,..., Tn) is a family of polynomials in F[X] such that for all i, Ti is in F[X1,..., Xi], monic in Xi, and reduced modulo 〈T1,..., Ti−1〉. The degree of T is the product deg(T1, X1) · · · deg(Tn, Xn). These objects allow one to solve a variety of problems for systems of polynomial equations, see [7, 1, 10, 6, 12]. We are interested here in the complexity of operations modulo a given triangular set T. The first question is modular multiplication: given polynomials A, B reduced modulo T, compute AB mod T. Further operations involve families of triangular sets. The lexicographic Gröbner basis of an ideal I for a given variable order may not be triangular. The workaround is to decompose I as I = I1∩ · · ·∩Is, with pairwise coprime Ij, where each Ij admits a triangular basis. The decomposition is in general not unique, but there exists a canonical choice, the equiprojectable decomposition [4]. That said, the most useful notion of “inversion ” is quasiinverses: given A reduced modulo T, we decompose the ideal 〈T 〉 as I0 ∩ I1, where A is zero modulo I0 and invertible modulo I1; the output is the equiprojectable decompositions of I0, I1, and the inverse of A modulo the triangular sets that define I1. The next question is change of order: starting from T, we output the equiprojectable
An almostlineartime algorithm for approximate max flow in undirected graphs, and its . . .
"... In this paper we present an almost linear time algorithm for solving approximate maximum flow in undirected graphs. In particular, given a graph with m edges we show how to produce a 1−ε approximate maximum flow in time O(m 1+o(1) · ε −2). Furthermore, we present this algorithm as part of a general ..."
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Cited by 15 (7 self)
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In this paper we present an almost linear time algorithm for solving approximate maximum flow in undirected graphs. In particular, given a graph with m edges we show how to produce a 1−ε approximate maximum flow in time O(m 1+o(1) · ε −2). Furthermore, we present this algorithm as part of a
Constructing LinearSized Spectral Sparsification in AlmostLinear Time
"... We present the first almostlinear time algorithm for constructing linearsized spectral sparsification for graphs. This improves all previous constructions of linearsized spectral sparsification, which requires Ω(n2) time [1], [2], [3]. A key ingredient in our algorithm is a novel combination of t ..."
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Cited by 1 (0 self)
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We present the first almostlinear time algorithm for constructing linearsized spectral sparsification for graphs. This improves all previous constructions of linearsized spectral sparsification, which requires Ω(n2) time [1], [2], [3]. A key ingredient in our algorithm is a novel combination
Greedy Decoding for Statistical Machine Translation in Almost Linear Time
, 2003
"... We present improvements to a greedy decoding algorithm for statistical machine translation that reduce its time complexity from at least cubic (O(n^6) when applied navely) to practically linear time without sacrificing translation quality. We achieve this by integrating hypothesis evaluati ..."
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Cited by 33 (2 self)
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We present improvements to a greedy decoding algorithm for statistical machine translation that reduce its time complexity from at least cubic (O(n^6) when applied navely) to practically linear time without sacrificing translation quality. We achieve this by integrating hypothesis
Results 1  10
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4,199,526