This dissertation proposes new polynomial-time approximation algorithms for selected optimization problems, including network and classic... Show moreThis dissertation proposes new polynomial-time approximation algorithms for selected optimization problems, including network and classic graph problems. We employed distinct strategies and techniques to solve these problems. In Chapter 1, we consider a problem we term FCSA, which aims to find an optimum way how clients are assigned to servers such that the largest latency on an interactivity path between two clients (client 1 to server 1, server 1 to server 2, then server 2 to client 2) is minimized. We present a (3/2)-approximation algorithm for FCSA and a (3/2)-approximation algorithm when server capacity constraints are considered. In Chapter 2, we focus on two variants of the Steiner Tree Problem and present better approximation ratios using known algorithms. For the Steiner Tree with minimum number of Steiner points and bounded edge length problem, we provide a polynomial time algorithm with ratio 2.277. For the Steiner Tree in quasi-bipartite graphs, we improve the best-known approximation ratio to 298/245 . In Chapter 3, we address the problem of searching for a maximum weighted series-parallel subgraph in a given graph, and present a (1/2 + 1/60)-approximation for this problem. Although there is currently no known real-life application of this problem, it remains an important and challenging open question in the field. Show less
