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Questions about problems that entail selecting the best element from some set of available alternatives, and methods to solve them.
1
vote
1
answer
40
views
Optimizing for maximum intervals given a distance bound
Given an interval set $X = \{(s_1, e_1), \dotsc, (s_N, e_N)\}$ ordered such that $s_i \leq s_j$ and $e_i \leq e_j$ for all $i < j$ and an integer $b$, I would like to find a maximum sized subset $X' \ …
5
votes
2
answers
216
views
Constraint violation and efficiency in search
It seems that (in a broad sense) two approaches can be utilized to produce an algorithm for solving various optimization problems:
Start with a feasible solution and expand search until constraints …
6
votes
2
answers
916
views
Randomized Rounding of Solutions to Linear Programs
Integer linear programming (ILP) is an incredibly powerful tool in combinatorial optimization. …
23
votes
1
answer
2k
views
How fundamental are matroids and greedoids in algorithm design?
Initially, matroids were introduced to generalize the notions of linear independence of a collection of subsets $E$ over some ground set $I$. Certain problems that contain this structure permit greedy …