Brief announcement: Efficient approximation algorithms for computing k disjoint restricted shortest paths

Let G = (V, E) be a digraph with nonnegative integral cost and delay on each edge, s and t be two vertices, and D ∈ ℤ⁺₀ be a delay bound, the k disjoint Restricted Shortest Path (kRSP) problem is to compute k disjoint paths between s and t with the total cost minimized and the total delay bounded by D. In this paper, we first present a pseudopolynomial-time algorithm with a bifactor approximation ratio of (1, 2), then improve the algorithm to polynomial time with a bifactor ratio of (1 + ∈, 2 + ∈) for any fixed ∈ > 0, which is better than the current best approximation ratio (O(1 + γ),O(1 + ln1/γ)) for any fixed γ > 0 [3, 5]. To the best of our knowledge, this is the first constant-factor algorithm that almost strictly obeys kRSP constraint.