I don't think you can avoid a brute force approach

Although I agree that the general problem is likely NP complete, there are probably at least some things one might do,singly or in combination, to pick out more or less likely solutions (and hence improve the likelihood that the first of N solutions contains something close to the optimal solution - i.e. we limit he number of solutions tried to N since we don't have infinite computing resources). I don't have the time to really think these through (or relearn my linear algebra), but someone else might like to pick up the ball on these ideas:

• There are probably some special groups of data-flow matrices that could be quickly solved analytically by simplifying the dataflow matrix using using eigenvectors and other linear algebra techniques.
• It might help to calculate the distribution of data flow values and use the distribution to prioritize which combinations of rows and columns should be tried first.

Best, beth

Update: in response to JavaFan's "I don't see how that could help" note below, added clarification of reason for picking more or less likely solutions.

---

---

Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!

Titles consisting of a single word are discouraged, and in most cases are disallowed outright.

Read Where should I post X? if you're not absolutely sure you're posting in the right place.

Please read these before you post! —

• How do I compose an effective node title?
• How do I post a question effectively?
• Markup in the Monastery

Posts may use any of the Perl Monks Approved HTML tags:

a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr

You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)

	For:		Use:
	&		&
	<		&lt;
	>		&gt;
	[		&#91;
	]		&#93;

Link using PerlMonks shortcuts! What shortcuts can I use for linking?

See Writeup Formatting Tips and other pages linked from there for more info.