Improved approximations for maximum independent set via approximation chains

Improved Approximations for Maximum Independent Set via Approximation Chains

We first define the notion of approximation chain and then we use it to obtain, in polynomial time, asymptotic approximation ratio of min{κ/μ, [κ′ log(log ∆)]/∆} (where κ is a fixed positive constant, κ′ is a constant depending on κ, and ∆, μ are the maximum and the average degrees of the graph, respectively). This result essentially improves, from both complexity and approximation quality poin...

Distributed Approximation of Maximum Independent Set and Maximum Matching

We present a simple distributed ∆-approximation algorithm for maximum weight independent set (MaxIS) in the CONGEST model which completes in O(MIS(G) · logW ) rounds, where ∆ is the maximum degree, MIS(G) is the number of rounds needed to compute a maximal independent set (MIS) on G, and W is the maximum weight of a node. Plugging in the best known algorithm for MIS gives a randomized solution ...

Faster Approximation for Maximum Independent Set on Unit Disk Graph

Maximum independent set from a given set D of unit disks intersecting a horizontal line can be solved in O(n) time and O(n) space. As a corollary, we design a factor 2 approximation algorithm for the maximum independent set problem on unit disk graph which takes both time and space of O(n). The best known factor 2 approximation algorithm for this problem runs in O(n logn) time and takes O(n) sp...

Improved Approximations of Independent Dominating Set in Bounded Degree Graphs

We consider the problem of nding an independent dominating set of minimum cardinality in bounded degree and regular graphs. We rst give an approximation algorithm for at most cubic graphs, that achieves ratio 2, based on greedy and local search techniques. We then propose an heuristic based on an iterative application of the greedy technique on graphs of lower and lower degree. When the graph i...

Heuristics for Maximum Clique and Independent Set