Algorithm 29 efficient algorithms for doubly and multiply restricted partitions

Riha, W.; James, Kevin R.

doi:10.1007/bf02241987

Cited by 10 publications

(4 citation statements)

References 3 publications

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“…Several algorithms are known to generate descending k-compositions in lexicographic [19,58], reverse lexicographic [43], and minimal-change [45] order. Hindenburg's eighteenth century algorithm [13, p.106] generates ascending kcompositions in lexicographic order and is regarded as the canonical method to generate partitions into a fixed number of parts: see Knuth [27,p.2], Andrews [4, p.232] or Reingold, Nievergelt & Deo [42, p.191].…”

Section: Related Workmentioning

confidence: 99%

Generating All Partitions: A Comparison Of Two Encodings

Kelleher¹,

O’Sullivan²

2009

Preprint

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Integer partitions may be encoded as either ascending or descending compositions for the purposes of systematic generation. Many algorithms exist to generate all descending compositions, yet none have previously been published to generate all ascending compositions. We develop three new algorithms to generate all ascending compositions and compare these with descending composition generators from the literature. We analyse the new algorithms and provide new and more precise analyses for the descending composition generators. In each case, the ascending composition generation algorithm is substantially more efficient than its descending composition counterpart. We develop a new formula for the partition function p(n) as part of our analysis of the lexicographic succession rule for ascending compositions.

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Section: Related Workmentioning

confidence: 99%

Generating All Partitions: A Comparison Of Two Encodings

Kelleher¹,

O’Sullivan²

2009

Preprint

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“…Many algorithms for the enumeration or random generation of combinatorial objects can be found in the literature. In particular, sequential algorithms for the generation of all partitions of a given integer, either in general or subject to some restrictions, may be found in [11,15,12,[4][5][6]17]. As mentioned above, Ref.…”

Section: Introductionmentioning

confidence: 99%

Parallel Algorithms for Counting and Randomly Generating Integer Partitions

Sanchis

Squire

1996

Journal of Parallel and Distributed Computing

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“…The problem of determining the different combinations of baud lengths amounts to the problem of generating all integer partitions for L (Kelleher and O'Sullivan, 2009). When additional constraints to baud lengths are applied, the problem is called the multiply restricted integer partitioning problem (Riha and James, 1976). An efficient algorithm for iterating through restricted partitions has been described by Riha and James (1976).…”

Section: Example: Range Spread Coherent Targetmentioning

confidence: 99%

Fractional baud-length coding

Vierinen¹

2011

Ann. Geophys.

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Abstract. We present a novel approach for modulating radar transmissions in order to improve target range and Doppler estimation accuracy. This is achieved by using non-uniform baud lengths. With this method it is possible to increase subbaud range-resolution of phase coded radar measurements while maintaining a narrow transmission bandwidth. We first derive target backscatter amplitude estimation error covariance matrix for arbitrary targets when estimating backscatter in amplitude domain. We define target optimality and discuss different search strategies that can be used to find well performing transmission envelopes. We give several simulated examples of the method showing that fractional baudlength coding results in smaller estimation errors than conventional uniform baud length transmission codes when estimating the target backscatter amplitude at sub-baud range resolution. We also demonstrate the method in practice by analyzing the range resolved power of a low-altitude meteor trail echo that was measured using a fractional baud-length experiment with the EISCAT UHF system.

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Algorithm 29 efficient algorithms for doubly and multiply restricted partitions

Cited by 10 publications

References 3 publications

Generating All Partitions: A Comparison Of Two Encodings

Generating All Partitions: A Comparison Of Two Encodings

Parallel Algorithms for Counting and Randomly Generating Integer Partitions

Fractional baud-length coding

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