Given a graph G = (V ,E) with node weight w : V → R+ and a subset S ⊆ V , find a minimum total weight tree interconnecting all nodes in S. This is the node-weighted Steiner tree problem which will be studied in this paper. In general, this problem is NP-hard and cannot be approximated by a polynomial time algorithm with performance ratio a lnn for any 0 < a < 1 unless NP ⊆ DTIME(nO(logn)), wher...

We prove that the genome aliquoting problem, the problem of finding a recent polyploid ancestor of a genome, with breakpoint distance can be solved in polynomial time. We propose an aliquoting algorithm that is a 2-approximation for the genome aliquoting problem with double cut and join distance, improving upon the previous best solution to this problem, Feijão and Meidanis' 4-approximation alg...

L max , a problem closely related to 1jr j jL max , which we will deene below. This will provide a rst example of a PTAS. In later lectures, we will exploit the technique of dynamic programming to develop other PTASs. 1 Approximation Schemes Finding a polynomial time optimization algorithm for a NP-hard optimization problem would imply that P = NP. Thus, given the widely held conjecture, that P...

We study the behavior of best simultaneous (lq , Lp)-approximation by rational functions on an interval, when the measure tends to zero. In addition, we consider the case of polynomial approximation on a finite union of intervals. We also get an interpolation result.

A new fully polynomial approximation scheme (FPTAS) is presented for the classical 0{1 knapsack problem. It considerably improves the space requirements. The two best previously known approaches need O(n+1=" 3) and O(n1=") space, respectively. Our new approximation scheme requires only O(n + 1=" 2) space while also reducing the running time.

We present a polynomial-time approximation algorithm for legally coloring as many edges of a given simple graph as possible using two colors. It achieves an approximation ratio of 24 29 ≈ 0.828. This improves on the previous best ratio of 468 575 ≈ 0.814.

We present a polynomial-time approximation algorithm for legally coloring as many edges of a given simple graph as possible using two colors. It achieves an approximation ratio of 468 575 . This improves on the previous best (trivial) ratio of 45 .