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Near-Linear Time Algorithm for $n$-Fold ILPs via Color Coding
2020
SIAM Journal on Discrete Mathematics
We study an important case of ILPs max{c T x | Ax = b, l ≤ x ≤ u, x ∈ Z nt } with n · t variables and lower and upper bounds , u ∈ Z nt . In n-fold ILPs non-zero entries only appear in the first r rows of the matrix A and in small blocks of size s × t along the diagonal underneath. Despite this restriction many optimization problems can be expressed in this form. It is known that n-fold ILPs can be solved in FPT time regarding the parameters s, r, and ∆, where ∆ is the greatest absolute value
doi:10.1137/19m1303873
fatcat:3ysplkmrw5gbfc7cdmvfkowau4