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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 …
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 …
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 …
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
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 …