On the longest increasing subsequence of a circular list

Albert, Michael H.; Atkinson, M. D.; Nussbaum, Doron; Sack, Jörg-Rüdiger; Santoro, Nicola

doi:10.1016/j.ipl.2006.08.003

Cited by 18 publications

(18 citation statements)

References 10 publications

(7 reference statements)

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“…This problem has been considered by Albert et al [2], who gave a Monte Carlo randomised algorithm, running in time O(n 1.5 log n) with small error probability.…”

Section: Cyclic Lcs Between Permutationsmentioning

confidence: 99%

Fast Distance Multiplication of Unit-Monge Matrices

Tiskin

2013

Algorithmica

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Monge matrices play a fundamental role in optimisation theory, graph and string algorithms. Distance multiplication of two Monge matrices of size n can be performed in time O(n 2 ). Motivated by applications to string algorithms, we introduced in previous works a subclass of Monge matrices, that we call simple unit-Monge matrices. We also gave a distance multiplication algorithm for such matrices, running in time O(n 1.5 ). Landau asked whether this problem can be solved in linear time. In the current work, we give an algorithm running in time O(n log n), thus approaching an answer to Landau's question within a logarithmic factor. The new algorithm implies immediate improvements in running time for a number of algorithms on strings and graphs. In particular, we obtain an algorithm for finding a maximum clique in a circle graph in time O(n log 2 n), and a surprisingly efficient algorithm for comparing compressed strings. We also point to potential applications in group theory, by making a connection between unit-Monge matrices and Coxeter monoids. We conclude that unit-Monge matrices are a fascinating object and a powerful tool, that deserve further study from both the mathematical and the algorithmic viewpoints.

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“…This problem has been considered by Albert et al [2], who gave a Monte Carlo randomised algorithm, running in time O(n 1.5 log n) with small error probability.…”

Section: Cyclic Lcs Between Permutationsmentioning

confidence: 99%

Fast Distance Multiplication of Unit-Monge Matrices

Tiskin

2013

Algorithmica

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“…Because consecutive slots have a different payload efficiency, the items in the sequence need to be weighted, and, the algorithm needs to take into account the wrap-around that occurs at the end of the slot table. In some respects the wrap-around is similar to the problem described in [27]. The first requirement does not introduce significant changes into the algorithm, but for the second, the algorithm will have to be applied repeatedly in a window which slides over the set of paths.…”

Section: B In-order Deliverymentioning

confidence: 99%

Multi-path routing in time-division-multiplexed networks on chip

Stefan

Goossens

2009

2009 17th IFIP International Conference on Very Large Scale Integration (VLSI-SoC)

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Abstract-The exponential increase in transistor count due to technological progress has resulted in an increase in complexity and processing power of on-chip elements. Recently a stage has been reached where it is not practical anymore to increase the core size, and as a consequence the number of cores, processing elements or peripherals is being increased instead. In this study we focus on improving the efficiency of a network between those processing elements using alternative routing strategies. We focus on a multi-path slot allocation method in networks with static resource reservations, in particular networks on chip (NoC) employing time-division multiplexing (TDM). The simplicity of these networks makes it possible to implement this routing scheme without significant hardware overhead. Our proposed method, although displaying large variations between test cases, provides significant overall gains in terms of allocated bandwidth, with an average gain across all tests of 29% against an exhaustive search of single-path routes, and gains of 47% when compared to other single-path routing algorithms.

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“…This problem has been considered by Albert et al [5], who gave a Monte Carlo randomised algorithm, running in time O(n 1.5 log n) with small error probability.…”

Section: Cyclic Lcs Between Permutationsmentioning

confidence: 99%

“…The overall running time is dominated by the call to Algorithm 4, which runs in time O(n log 2 n). A version of the cyclic LCS problem between permutations, parameterised by the output LCS length l, has also been considered by Albert et al [5], who gave an algorithm running in time O(nl log n). This was improved upon by Deorowicz [39], who gave an algorithm running in time O min(nl, n log n + l 3 log n) .…”

Section: Cyclic Lcs Between Permutationsmentioning

confidence: 99%

Semi-local String Comparison: Algorithmic Techniques and Applications

Tiskin

2008

Math.comput.sci.

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The longest common subsequence (LCS) problem is a classical problem in computer science. The semi-local LCS problem is a generalisation of the LCS problem, arising naturally in the context of string comparison. In this work, we present a number of algorithmic techniques related to the semi-local LCS problem, and give a number of algorithmic applications of these techniques. Summarising the presented results, we conclude that semilocal string comparison turns out to be a useful algorithmic plug-in, which unifies, and often improves on, a number of previous approaches to various substring-and subsequence-related problems.

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On the longest increasing subsequence of a circular list

Cited by 18 publications

References 10 publications

Fast Distance Multiplication of Unit-Monge Matrices

Fast Distance Multiplication of Unit-Monge Matrices

Multi-path routing in time-division-multiplexed networks on chip

Semi-local String Comparison: Algorithmic Techniques and Applications

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