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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.

3 votes
1 answer
238 views

Effect on connectivity when partitioning a graph

I have a connected graph $G=(V,E)$, $V$ being the vertex set and $E$ being the edge set. I partition the graph into components $C=\{C_1,\dots,C_n\}$ such that all $C_i$ are pairwise disjoint. Take t …
Opt's user avatar
  • 601
2 votes

Minimal Backtracking Proof Tree

I found a reference which proves that minimum propositional proof length is NP-hard to linearly approximate for a variety of systems from resolution proofs to Frege proofs. Minimal Propositional Proof …
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  • 601
5 votes
1 answer
539 views

Minimal Backtracking Proof Tree

When trying to prove that a particular instance of a problem like graph coloring or SAT is unsatisfiable, generally one explores the search tree using an algorithm like DPLL and the proof of unsatisfi …
Opt's user avatar
  • 601
4 votes
1 answer
8k views

Number of Shortest paths problem

Hey, Is countinng the number of shortest paths in a weighted directed acyclic graph with nonnegative weights #P-complete? If so, is there a proof I can read somewhere? Thanks
Opt's user avatar
  • 601
5 votes
3 answers
2k views

Number of paths equal less than equal to a certain length

Hey, I need to count the number of paths from node $s$ to $t$ in a weighted directed acyclic graph s.t. the total weight of each path is less than or equal to a certain weight $W$. I have an algorith …
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  • 601