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Near-Linear Time Algorithm for n-fold ILPs via Color Coding
[article]
2018
arXiv
pre-print
We study an important case of ILPs {c^Tx Ax = b, l ≤ x ≤ u, x ∈Z^n t} with n· t variables and lower and upper bounds ℓ, 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 Δ, where Δ is the greatest absolute value of an entry
arXiv:1811.00950v1
fatcat:3gkpu5p3gvdqpk6z4aeriqqej4