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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.

2 votes
1 answer
208 views

Covering set problem

All the references I can find to Covering Set appear to be algorithmic. Is there are any reference for the simple existential question --- Suppose we have $k$ sets $X_1,…,X_k$ which are subsets of a …
David Harris's user avatar
  • 3,475
3 votes
2 answers
856 views

Formal verification in complexity theory

Reading books and papers on complexity theory, I am struck by the extreme degree to which proofs are stated in an intuitive, hand-wavy way. The alternative is to give a lot of details about the coding …
David Harris's user avatar
  • 3,475
14 votes
3 answers
3k views

Definition of relativization of complexity class

Is there any general definition, for a class $C$ of languages, what is the relativized class $C^A$ for an oracle $A$? Usually, these classes and their relativizations seem to be defined in an ad-hoc …
David Harris's user avatar
  • 3,475
3 votes
0 answers
364 views

Amortized analysis of data structure via potential function

One common method for proving that a data structure supports an operation in $O(f(n))$ amortized time is to construct a potential function $\Phi: \mathcal S \rightarrow \mathbf R^{+}$, which associate …
David Harris's user avatar
  • 3,475
5 votes
0 answers
572 views

When is polytope compatible with network flow?

A linear program is the problem of optimizing an linear objective function within some polytope $A$ over $\mathbf R^n$. My question is motivated by the question of when a linear programming problem ca …
David Harris's user avatar
  • 3,475