Design of Self-Stabilizing Approximation Algorithms via a Primal-Dual Approach

Self-stabilization is an important concept in the realm of fault-tolerant distributed computing. In this paper, we propose a new approach that relies on the properties of linear programming duality to obtain self-stabilizing approximation algorithms for distributed graph optimization problems. The power of this new approach is demonstrated by the following results: A self-stabilizing 2(1 + ε)-approximation algorithm for minimum weight vertex cover that converges in O(log ∆/(ε log log ∆)) synchronous rounds. A self-stabilizing ∆-approximation algorithm for maximum weight independent set that converges in O(∆ + log^∗ n) synchronous rounds. A self-stabilizing ((2ρ + 1)(1 + ε))-approximation algorithm for minimum weight dominating set in ρ-arboricity graphs that converges in O((log ∆)/ε) synchronous rounds. In all of the above, ∆ denotes the maximum degree. Our technique improves upon previous results in terms of time complexity while incurring only an additive O(log n) overhead to the message size. In addition, to the best of our knowledge, we provide the first self-stabilizing algorithms for the weighted versions of minimum vertex cover and maximum independent set.