Approximating the discrete time-cost tradeoff problem with bounded depth

Abstract We revisit the deadline version of discrete time-cost tradeoff problem for special case bounded depth. Such instances occur example in VLSI design. The depth an instance is number jobs a longest chain and denoted by d . prove new upper lower bounds on approximability. First we observe that can be regarded as finding minimum-weight vertex cover -partite hypergraph. Next, study natural LP relaxation, which solved polynomial time fixed and—for instances—up to arbitrarily small error general. Improving prior work Lovász Aharoni, Holzman Krivelevich, describe deterministic algorithm with approximation ratio slightly less than $$\frac{d}{2}$$ d 2 hypergraphs given -partition. This tight yields also -approximation general instances, even if not fixed. inapproximability show no better $$\frac{d+2}{4}$$ + 4 possible, assuming Unique Games Conjecture $$\text {P}\ne \text {NP}$$ P ≠ NP strengthens result Svensson [21], who showed under same assumptions constant-factor exists (of unbounded depth). Previously, only APX-hardness was known