# Questions tagged [algorithms]

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.

**73**

**17**answers

### Examples of algorithms requiring deep mathematics to prove correctness

**52**

**1**answer

### How to be rigorous about combinatorial algorithms?

**50**

**4**answers

### What algorithm in algebraic geometry should I work on implementing?

**47**

**4**answers

### How hard is it to compute the number of prime factors of a given integer?

**44**

**1**answer

### improving known bounds for Pierce expansions; cash prize

**42**

**7**answers

### What is the time complexity of computing sin(x) to t bits of precision?

**40**

**4**answers

### Why is “P vs. NP” necessarily relevant?

**39**

**2**answers

### How fast can we *really* multiply matrices?

**36**

**10**answers

### Algorithm for finding the volume of a convex polytope

**35**

**14**answers

### What are the Applications of Hypergraphs

**34**

**5**answers

### Computing the Galois group of a polynomial

**33**

**19**answers

### What is the easiest randomized algorithm to motivate to the layperson?

**32**

**1**answer

### Does the algorithm of the Greeks produce all prime numbers?

**32**

**2**answers

### Does anyone want a pretty Maass form?

**31**

**9**answers

### Fast Matrix Multiplication

**31**

**3**answers

### Are surjectivity and injectivity of polynomial functions from $\mathbb{Q}^n$ to $\mathbb{Q}$ algorithmically decidable?

**30**

**3**answers

### Can assignment solve stable marriage?

**30**

**1**answer

### An edge partitioning problem on cubic graphs

**29**

**5**answers

### Is there an algorithm for determining whether an expression involving nested radicals is rational?

**28**

**3**answers

### Is it decidable whether or not a collection of integer matrices generates a free group?

**28**

**0**answers

### On certain representations of algebraic numbers in terms of trigonometric functions

**27**

**1**answer

### Is this BBP-type formula for $\ln 257$ and $\ln 65537$ true?

**27**

**1**answer

### Decidability of equality of expressions built using 1,+,-,*,/,^

**26**

**5**answers

### What is a good method to find random points on the n-sphere when n is large?

**26**

**4**answers

### Can Gröbner bases be used to compute solutions to large, real-world problems?

**26**

**2**answers

### A small unavoidable collection of subgraphs

**25**

**2**answers

### Distinct numbers in multiplication table

**25**

**2**answers

### Groebner basis with group action

**24**

**3**answers

### Changing the signs of the coefficients of a polynomial to make all the roots real

**24**

**0**answers

### Decidability of equality of elementary expressions

**23**

**5**answers

### Securing privacy of “who communicates with whom” under Orwell-like conditions

**23**

**4**answers

### Groups where word problem is solvable, but not quickly?

**22**

**5**answers

### Fastest Algorithm to Compute the Sum of Primes?

**22**

**3**answers

### Can one measure the infeasibility of four color proofs?

**22**

**4**answers

### does the “convolution theorem” apply to weaker algebraic structures?

**22**

**4**answers

### Complexity of testing integer square-freeness

**21**

**4**answers

### Finding a cycle of fixed length

**21**

**1**answer

### Evidence for integer factorization is in $P$

**21**

**3**answers

### Is there a way of canonically labelling permutation groups?

**20**

**1**answer

### How hard is it to compute the Euler totient function?

**20**

**3**answers

### Satisfiability of general Boolean formulas with at most two occurrences per variable

**20**

**3**answers

### Easy functions?

**19**

**9**answers

### How can I generate random permutations of [n] with k cycles, where k is much larger than log n?

**19**

**5**answers

### Algorithms for finding rational points on an elliptic curve?

**19**

**1**answer

### “Gauss trick” vs Karatsuba multiplication

**19**

**4**answers

### FFTs over finite fields?

**19**

**3**answers

### A generalization of the triangle counting problem for simple weighted graphs

**18**

**12**answers

### Lower Bounds in Theoretical Computer Science

**18**

**8**answers

### Determine if circle is covered by some set of other circles

**18**

**2**answers