An approximate version of a conjecture of Aharoni and Berger

AbstractA diregular bipartite tournament is a balanced complete bipartite graph whose edges are oriented so that every vertex has the same in- and out-degree. In 1981 Jackson showed that a diregular bipartite tournament contains a Hamilton cycle, and conjectured that in fact its edge set can be partitioned into Hamilton cycles. We prove an approximate version of this conjecture: for every ε > 0 there exists n0 such that every diregular bipartite tournament on 2n ≥ n0 vertices contains a collection of (1/2–ε)n cycles of length at least (2–ε)n. Increasing the degree by a small proportion allows us to prove the existence of many Hamilton cycles: for every c > 1/2 and ε > 0 there exists n0 such that every cn-regular bipartite digraph on 2n ≥ n0 vertices contains (1−ε)cn edge-disjoint Hamilton cycles.

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On computational complexity of construction of c -optimal linear regression models over finite experimental domains

Tatra Mountains Mathematical Publications ◽

10.2478/v10127-012-0002-3 ◽

2012 ◽

Vol 51 (1) ◽

pp. 11-21

Author(s):

Jaromír Antoch ◽

Michal Černý ◽

Milan Hladík

Keyword(s):

Linear Programming ◽

Regression Models ◽

Parallel Implementation ◽

Optimal Designs ◽

Polynomial Algorithms ◽

Linear Regression Models ◽

Optimal Linear ◽

New Algorithms ◽

Approximate Version ◽

Strongly Polynomial

ABSTRACT Recent complexity-theoretic results on finding c-optimal designs over finite experimental domain X are discussed and their implications for the analysis of existing algorithms and for the construction of new algorithms are shown. Assuming some complexity-theoretic conjectures, we show that the approximate version of c-optimality does not have an efficient parallel implementation. Further, we study the question whether for finding the c-optimal designs over finite experimental domain X there exist a strongly polynomial algorithms and show relations between considered design problem and linear programming. Finally, we point out some complexity-theoretic properties of the SAC algorithm for c-optimality.

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Weak sequential convergence in L1(μ, X) and an approximate version of Fatou's Lemma

Journal of Mathematical Analysis and Applications ◽

10.1016/0022-247x(86)90108-3 ◽

1986 ◽

Vol 114 (2) ◽

pp. 569-573 ◽

Cited By ~ 26

Author(s):

M.Ali Khan ◽

Mukul Majumdar

Keyword(s):

Sequential Convergence ◽

Fatou’S Lemma ◽

Fatou's Lemma ◽

Approximate Version

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Two Efficient Techniques to Find Approximate Overlaps between Sequences

BioMed Research International ◽

10.1155/2017/2731385 ◽

2017 ◽

Vol 2017 ◽

pp. 1-8

Author(s):

Maan Haj Rachid

Keyword(s):

Hamming Distance ◽

Pigeonhole Principle ◽

Huge Number ◽

Three Solutions ◽

Approximate Matching ◽

Prefix Tree ◽

Error Detecting ◽

Next Generation Sequencing Ngs ◽

Generation Sequencing ◽

Approximate Version

The next-generation sequencing (NGS) technology outputs a huge number of sequences (reads) that require further processing. After applying prefiltering techniques in order to eliminate redundancy and to correct erroneous reads, an overlap-based assembler typically finds the longest exact suffix-prefix match between each ordered pair of the input reads. However, another trend has been evolving for the purpose of solving an approximate version of the overlap problem. The main benefit of this direction is the ability to skip time-consuming error-detecting techniques which are applied in the prefiltering stage. In this work, we present and compare two techniques to solve the approximate overlap problem. The first adapts a compact prefix tree to efficiently solve the approximate all-pairs suffix-prefix problem, while the other utilizes a well-known principle, namely, the pigeonhole principle, to identify a potential overlap match in order to ultimately solve the same problem. Our results show that our solution using the pigeonhole principle has better space and time consumption over an FM-based solution, while our solution based on prefix tree has the best space consumption between all three solutions. The number of mismatches (hamming distance) is used to define the approximate matching between strings in our work.

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An approximate version of Sumnerʼs universal tournament conjecture

Journal of Combinatorial Theory Series B ◽

10.1016/j.jctb.2010.12.006 ◽

2011 ◽

Vol 101 (6) ◽

pp. 415-447 ◽

Cited By ~ 9

Author(s):

Daniela Kühn ◽

Richard Mycroft ◽

Deryk Osthus

Keyword(s):

Approximate Version

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Circumcentering approximate reflections for solving the convex feasibility problem

Fixed Point Theory and Algorithms for Sciences and Engineering ◽

10.1186/s13663-021-00711-6 ◽

2022 ◽

Vol 2022 (1) ◽

Author(s):

G. H. M. Araújo ◽

R. Arefidamghani ◽

R. Behling ◽

Y. Bello-Cruz ◽

A. Iusem ◽

...

Keyword(s):

Convex Sets ◽

Classical Method ◽

Computational Cost ◽

Linear Convergence ◽

Feasibility Problem ◽

Reflection Method ◽

Convex Feasibility ◽

Method Of Alternating Projections ◽

Low Computational Cost ◽

Approximate Version

AbstractThe circumcentered-reflection method (CRM) has been applied for solving convex feasibility problems. CRM iterates by computing a circumcenter upon a composition of reflections with respect to convex sets. Since reflections are based on exact projections, their computation might be costly. In this regard, we introduce the circumcentered approximate-reflection method (CARM), whose reflections rely on outer-approximate projections. The appeal of CARM is that, in rather general situations, the approximate projections we employ are available under low computational cost. We derive convergence of CARM and linear convergence under an error bound condition. We also present successful theoretical and numerical comparisons of CARM to the original CRM, to the classical method of alternating projections (MAP), and to a correspondent outer-approximate version of MAP, referred to as MAAP. Along with our results and numerical experiments, we present a couple of illustrative examples.

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On customer flows in jackson queueing networks

Advances in Applied Probability ◽

10.1017/s0001867800004535 ◽

2010 ◽

Vol 42 (04) ◽

pp. 1094-1101

Author(s):

Sen Tan ◽

Aihua Xia

Keyword(s):

Poisson Distribution ◽

Queueing Networks ◽

Queueing Network ◽

Equilibrium Flow ◽

Small Probability ◽

Flow Process ◽

Cluster Process ◽

Poisson Cluster Process ◽

Poisson Cluster ◽

Approximate Version

Melamed's theorem states that, for a Jackson queueing network, the equilibrium flow along a link follows a Poisson distribution if and only if no customers can travel along the link more than once. Barbour and Brown (1996) considered the Poisson approximate version of Melamed's theorem by allowing the customers a small probability p of travelling along the link more than once. In this note, we prove that the customer flow process is a Poisson cluster process and then establish a general approximate version of Melamed's theorem that accommodates all possible cases of 0 ≤ p < 1.

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Loose Hamiltonian cycles forced by ( k − 2)-degree – approximate version

Electronic Notes in Discrete Mathematics ◽

10.1016/j.endm.2016.09.056 ◽

2016 ◽

Vol 54 ◽

pp. 325-330

Author(s):

J. de O. Bastos ◽

G.O. Mota ◽

M. Schacht ◽

J. Schnitzer ◽

F. Schulenburg

Keyword(s):

Hamiltonian Cycles ◽

Approximate Version

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Finite‐difference migration derived from the Kirchhoff‐Helmholtz integral

Geophysics ◽

10.1190/1.1444063 ◽

1996 ◽

Vol 61 (5) ◽

pp. 1394-1399 ◽

Cited By ~ 1

Author(s):

Thomas Rühl

Keyword(s):

Wave Equation ◽

Finite Difference ◽

Continued Fraction ◽

Velocity Fields ◽

Finite Difference Schemes ◽

Square Root ◽

Continued Fraction Expansion ◽

The One ◽

Root Operator ◽

Approximate Version

Finite‐difference (FD) migration is one of the most often used standard migration methods in practice. The merit of FD migration is its ability to handle arbitrary laterally and vertically varying macro velocity fields. The well‐known disadvantage is that wave propagation is only performed accurately in a more or less narrow cone around the vertical. This shortcoming originates from the fact that the exact one‐way wave equation can be implemented only approximately in finite‐difference schemes because of economical reasons. The Taylor or continued fraction expansion of the square root operator in the one‐way wave equation must be truncated resulting in an approximate version of the one‐way wave equation valid only for a restricted angle range.

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