For positive-integer two-size Gasoline instances with deliveries in {1,K}, the position-first iterative-rounding algorithm under the doubly stochastic assignment-LP interpretation has capacity at most OPT+K−2.
For positive-integer two-size Gasoline instances with deliveries in {1,K}, the position-first iterative-rounding algorithm under the doubly stochastic assignment-LP interpretation has capacity at most OPT+K−2. For K≥3, the original-index tie rule has matching instances with OPT=K and returned capacity 2K−2, giving worst-case ratio 2−2/K.
For positive-integer two-size Gasoline instances with deliveries in {1,K}, the position-first iterative-rounding algorithm under the doubly stochastic assignment-LP interpretation has capacity at most OPT+K−2. For K≥3, the original-index tie rule has matching instances with OPT=K and returned capacity 2K−2, giving worst-case ratio 2−2/K.
If correct, proves the two-size conjecture and identifies the exact worst-case ratio for the stated tie rule.
Is iterative rounding a factor-two approximation for positive-integer Gasoline instances with delivery sizes {1,K}, and what is its sharp ratio?
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