Date  File  Comment by  Comment  Rating 

10 Mar 2014  Restricted Integer Composition Generates restricted and unrestricted integer compositions  iuvaris  Well, it's still my firm view that this algorithm (not the implementation) is awfully slow and no bit more general than other algorithms for restricted integer compositions. For example, when I set n=16; a=1; b=4; and run tic; jdoric(n,1,16,a,b); toc this yields, on my computer, a run time of 21 seconds. Contrarily, when I run tic; for k=1:16; colex(n,k,a,b); toc this runs in 2.5 seconds. (Colex is the Vajnovszki/Vernay algorithm that is also available as a matlab implementation). When I set n=18, run times become 289 seconds and 25.6 seconds, respectively. So, why on earth would anyone want to use this slow algorithm? Other issues:


13 Jan 2014  Restricted Integer Composition Generates restricted and unrestricted integer compositions  iuvaris  Alright, I agree, John D'Errico, that the argumentation should remain factual. It's just really difficult to argue with Mr. Opdyke because he apparently doesn't understand some basic principles of the things he has published about. Writing problematic papers is one thing, defending errors beyond reason is another. Whatever his contributions in his paper have been, they have neither been the provision of solutions to open problems nor the provision of a general algorithm for solving the restricted integer composition/partition problem. I think that the "success" of his paper is due to selfpromotion  and recipients of his work should be made aware of his paper's and algorithm's deficiencies. In the interest of his readers, I have summarized my points of critique in a pdf file.


12 Jan 2014  Restricted Integer Composition Generates restricted and unrestricted integer compositions  iuvaris  Lastly, JD Opdyke, why do you never mention hirosh tagoya, Mark Headstrom, Nam Quire, Jasper Baxxter? It's seems your mathwork comments are just as suspicious as your journal publication. 

10 Jan 2014  Restricted Integer Composition Generates restricted and unrestricted integer compositions  iuvaris  Well, it is really extremely simple. The JD Opdyke paper has the following major flaws: 1) The Odyke algorithm takes O(k) time per composition of n with k parts. Thus, the algorithm is inefficient. 2) The counting formulae are copied from previous work and sold as new. It is wellknown that the number of compositions of n with k parts, each in a set A, satisfies the recursion: c_A(n,k) = sum_{a in A} c_A(na,k1) (see Heubach and Mansour, Compositions of n with parts in a set A, Proof of Theorem 2.1)
3) All errors made concerning compositions translate to partitions (which are just ordered compositions) 4) An algorithm that runs in time O(k) per composition needs not solve the restricted integer composition problem in its full generality (arbitrary lower and upper bounds a and b) since the general case can be reduced to a=0. 5) To worsen things for the Opdyke paper, the algorithm solves the problem with upper and lower bounds on the NUMBER OF PARTS in a quite silly way by simply invoking the inefficient Opdyke algorithm for each part. 6) This said, the Vajnovszki algorithm is trivially as general as the Opdyke algorithm is and runs incredibly much faster as k increases since it is not inefficient. 

06 Dec 2013  Sequence alignment with arbitrary steps Determine the best alignment, with allowed 'steps' <S>, between two sequences  iuvaris  In the below example, the alignment will be (formatting has been lost below) x  y 1  1 3


06 Dec 2013  Sequence alignment with arbitrary steps Determine the best alignment, with allowed 'steps' <S>, between two sequences  iuvaris  Sample usage would be x=[1,2,2,3,3,2,1,2];
steps = [1 1; % substitution/identity
function sim=mysimilarity(sub1,sub2);
sim=2;
if isequal([k1 k2],[1 1])
if isequal([k1 k2],[2 2])
if isequal([k1 k2],[1 2])  isequal([k1 k2],[2 1])
end


06 Nov 2013  Restricted Integer Composition Generates restricted and unrestricted integer compositions  iuvaris  Again, you may want to look at http://www.mathworks.com/matlabcentral/fileexchange/44186restrictedintegercompositionswithfixednumberofparts for a potentially much faster algorithm based on a different paper. 

06 Nov 2013  Restricted Integer Composition Generates restricted and unrestricted integer compositions  iuvaris  First, thanks to the author for providing this implementation. However, both the implementation and the algorithm/paper it is based upon are problematic, from my point of view: (1) Line 41 of the algorithm reads as
which, if you compare it with the pseudocode in the Opdyke paper, is not correct (it should be cell(level+1)\le b). This is not the only mistake in the implementation. (2) In the description, it says that the implementation "[...] seems to work pretty fast for integers up to 100". Now, there are \binom{n1}{k1} integer compositions of an integer n with k parts and e.g. \binom{1001}{501} is 5.0446e+028. I would be really suprised if this algorithm were "pretty fast" at enumerating all these compositions. Concerning the Opdyke paper. From my perspective, this paper is highly suspicious and problematic: (a) The claims concerning the novel formulas that the paper "discovers" are factually wrong. This paper discovers no new formulas. It copies them from the work it cites.
k = 6
(d) Finally, it seems that the last couple of comments  those with pretty unusual language and which are so 'euphoric'  are written by the author of the Opdyke paper himself ... (e) To conclude, I think that this implementation is an accurate copy of the pseudocode presented in the Opdyke paper, with a few mistakes. However, I think that it is highly doubtful whether the Opdyke algorithm is efficient at all. Given the experiments I have outlined, I would judge that the Opdyke algorithm is of no practical value and cannot compete with current stateoftheart. 
