Dynamic Programming and Shortest Path

Ding-Zhu Du, Panos Pardalos, Xiaodong Hu and Weili Wu
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Ding-Zhu Du: University of Texas, Dallas
Panos Pardalos: University of Florida
Xiaodong Hu: Chinese Academy of Sciences
Weili Wu: University of Texas at Dallas

Chapter Chapter 3 in Introduction to Combinatorial Optimization, 2022, pp 43-73 from Springer

Abstract: Abstract A divide-and-conquer algorithm consists of many iterations. Usually, each iteration contains three steps. In the first step (called the divide step), divide the problem into smaller subproblems. In the second step (called conquer step), solve those subproblems. In the third step (called the combination step), combine solutions for subproblems into a solution for the original problem. Is it true that every algorithm with each iteration consisting of the above three steps belongs to the class of divide-and-conquer? The answer is No. In this chapter, we would like to introduce a class of algorithms, called dynamic programming. Every algorithm in this class consists of discrete iterations, each of which contains the divide step, the conquer step, and the combination step. However, they may not be the divide-and-conquer algorithms. Actually, their self-reducibility structure may not be a tree.

Date: 2022
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DOI: 10.1007/978-3-031-10596-8_3

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