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Results tagged with computational-complexity
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user 12481
This is a branch that includes: computational complexity theory; complexity classes, NP-completeness and other completeness concepts; oracle analogues of complexity classes; complexity-theoretic computational models; regular languages; context-free languages; Komolgorov Complexity and so on.
0
votes
Constructing Useful SAT Instances
I suppose by "literals" you mean variables.
If you allow additional temporary variables
there is explicit polynomial encoding in 4-SAT
by carefully constructing the CNF.
First we construct CNFs for …
- 25.4k
5
votes
1
answer
218
views
Complexity of counting MAXCUT in planar graphs -- seemingly contradicting claims
Confusion is likely. Appears to me two papers give contradicting claims
about the complexity of counting MAXCUT in planar graphs.
Exact Max 2-SAT: Easier and Faster p. 6
However, counting the num …
- 25.4k
2
votes
1
answer
180
views
Graph classes where finding explicit coloring have certificate that it is minumum
Graph coloring doesn't have certificate that smaller coloring doesn't exist in general.
I am looking for graph classes where finding explicit coloring is not polynomial and have polynomially verifiab …
- 25.4k
0
votes
Bounds for constructing $n!$ with additions, subtractions, and multiplications starting from...
Here is partial result about multiple of factorial
based on heuristic code.
By the paper Michael Stoll cites,
$t(m) \le 2 \log{m}$.
By repeated squaring $t(a^{2^k}) \le t(a)+k$.
Let $M=\log{n}$ an …
- 25.4k
2
votes
1
answer
161
views
Complexity of numerically solving systems over the reals
Basically I am interested in
What is the complexity of numerically solving systems over $\mathbb{R}$?
By solving I mean finding at least one numeric solution with given
precision.
Probably the …
- 25.4k
1
vote
0
answers
41
views
Complexity of finding algebraic dependency of polynomials over the rationals or in a finite ...
Let $f_1,\ldots f_m \in K[x_1,\ldots,x_n]$ where $K$ is $\mathbb{Q}$ or a finite field.
Q1 What is the complexity of finding all algebraic dependencies between $f_i$?
Q2 What is the complexity of fin …
- 25.4k
2
votes
0
answers
87
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Complexity consequence of logarithmic boolean width of co-bounded degree graphs?
The paper On graph classes with logarithmic
boolean-width claims that the
boolean width of co-k-degenerate graphs is at most $k\log{n}$
and a lot of graph vertex partition problems can be solved in
po …
- 25.4k
14
votes
5
answers
1k
views
Bounds for constructing $n!$ with additions, subtractions, and multiplications starting from...
Found this on Complexity Zoo warning expired certificate
check NP Over The Complex Numbers.
[BCS+97] show the following striking result. For a positive integer $n$, let $t(n)$ denote the minimum n …
- 25.4k
3
votes
0
answers
50
views
Complexity of OBDD isomorphism (representing same function after permutation of variables)?
According to wikipedia Ordered Binary Decision Diagarams (OBDD) are a data structure that is used to represent a Boolean function.
OBDD is a DAG with two sinks $0,1$.
The size of the BDD is number o …
- 25.4k
15
votes
1
answer
1k
views
Is deciding if one planar graph is dual to another really NP-hard (Wikipedia claim)?
Wikipedia claims (permanent link) without reference:
Testing whether one planar graph is dual to another is NP-complete.
Another claim with reference:
For any plane graph G, the medial graph …
- 25.4k
2
votes
NP-hardness of vertex cover for 3-chromatic graphs
Yes, it is NP-hard via reduction to Independent Set in cubic (3-regular) graphs.
Cubic graphs different from $K_4$ are 3-colorable in polynomial time via Brooks' theorem and IS remains NP-hard for the …
- 25.4k
0
votes
Complexity of a problem remotely related to the discrete logarithm $A=x g^x$
Recent arxiv paper The Discrete Lambert Map
makes analogy with the Lambert W function and suggests solving the
first will break the ElGamal crypto.
The authors found pattern in the solutions $\mod p …
- 25.4k
5
votes
Accepted
Can we solve Hamiltonian Path problem for biconnected planar graphs in linear time?
According to graph classes this is NP-complete even on 2-connected ∩ cubic ∩ planar.
The proof reduces it to NP-hardness of Hamiltonian cycle.
Added because of the edit.
I believe the graphclasse …
- 25.4k
11
votes
3
answers
491
views
Finite objects for which isomorphism is NP-hard or harder?
Are there finite objects for which deciding isomorphism
is NP-hard or harder?
Graphs and groups are not solutions.
Searching the web didn't return answer for me.
Partial result based on Chow's co …
- 25.4k
1
vote
1
answer
137
views
Complexity of edge coloring graphs with $\Delta(G) \ge n/3$ assuming the overfull conjecture
Closely related to this on cstheory.
Let $G$ be graph of order $n$ with $\Delta(G) \ge n/3$.
Assume the overfull conjecture.
Can we edge color $G$ with minimal number of colors in polynomial time?
…
- 25.4k