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Results tagged with algorithms
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user 24076
Informally, an algorithm is a set of explicit instructions used to solve a problem (e.g. Euclid's algorithm for computing the greatest common divisor of two integers). For more specific questions on algorithms, this tag may be used in conjunction with the approximation-algorithms, algorithmic-randomness and algorithmic-topology tags.
1
vote
How to solve tiling problem with dancing links?
The following recent paper shows that many problems involving packing geometric objects in the plane are $\exists\mathbb{R}$-complete:
Mikkel Abrahamsen, Tillmann Miltzow and Nadja Seiferth, Framework …
- 6,101
9
votes
Accepted
Exact coverability of $\mathbb{Z}_n$ by cyclic shifts of a given set -- easy? NP-complete?
Kolountzakis and Máté Matolcsi, Algorithms for translational tiling, Journal of Mathematics and Music, 3:2 (2009), 85-97, https://doi.org/10.1080/17459730903040899
Mihail N. …
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5
votes
Algorithms to count perfect matchings in near planar graphs
Graphs of bounded genus (both orientable or non-orientable):
G. Tesler, Matchings in Graphs on Non-orientable Surfaces, Journal of Combinatorial Theory, Series B,
Volume 78, Issue 2 (2000), 198-231.
h …
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5
votes
Accepted
Square filling self avoiding walk
The following paper by Umans and Lenhart gives a polynomial-time algorithm for finding a Hamiltonian cycle in "solid" grid graphs (grid graphs with no holes with area larger than $1$):
http://users.cm …
- 6,101
7
votes
Is there an efficient algorithm to check whether two matrices are the same up to row and col...
Regarding the first question: there is a counterexample of size $91$.
There are four non-isomorphic finite projective planes of order $9$: https://doi.org/10.1016/0012-365X(91)90280-F, http://oeis.or …
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45
votes
Issue UPDATE: in graph theory, different definitions of edge crossing numbers - impact on ap...
Assuming an unpublished Ramsey-type result by Robertson and Seymour about Kuratowski minors [FK18, Claim 5], which is now "folklore" in the graph-minor community,
an asymptotic variant of the crossing …
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