Introduction to Graph Convexity: An Algorithmic Approach
暫譯: 圖形凸性導論：算法方法

Araújo, Júlio, Dourado, Mitre C., Protti, Fábio

Introduction to Graph Convexity: An Algorithmic Approach
  • 出版商: Springer
  • 出版日期: 2025-05-13
  • 售價: $2,970
  • 貴賓價: 9.5 折 $2,822
  • 語言: 英文
  • 頁數: 152
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031841271
  • ISBN-13: 9783031841279
  • 相關分類: Algorithms-data-structures

    • 海外代購書籍(需單獨結帳)

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商品描述

This book focuses on the computational aspects of graph convexity, with a particular emphasis on path convexity within graphs. It provides a thoughtful introduction to this emerging research field, which originated by adapting concepts from convex geometry to combinatorics and has experienced substantial growth.

The book starts with an introduction of fundamental convexity concepts and then proceeds to discuss convexity parameters. These parameters fall into two categories: one derived from abstract convexity studies and another motivated by computational complexity. Subsequent chapters explore geometric convexity within graphs, examining various graph classes such as interval graphs, proper interval graphs, cographs, chordal graphs, and strongly chordal graphs. The text concludes with a study of the computation of convexity parameters across different convexity types, including practical applications in areas like game theory.

Compact and straightforward, this work serves as an ideal entry point for students and researchers interested in pursuing further research in the field of convexity.

The English translation of this book, originally in Portuguese, was facilitated by artificial intelligence. The content was later revised by the authors for accuracy.

商品描述(中文翻譯)

本書專注於圖形凸性（graph convexity）的計算方面，特別強調圖中的路徑凸性（path convexity）。它為這一新興研究領域提供了深思熟慮的介紹，該領域源於將凸幾何（convex geometry）的概念應用於組合數學（combinatorics），並經歷了顯著的增長。

本書首先介紹基本的凸性概念，然後討論凸性參數（convexity parameters）。這些參數分為兩類：一類源自抽象凸性研究，另一類則受到計算複雜性（computational complexity）的啟發。隨後的章節探討圖中的幾何凸性，檢視各種圖類別，如區間圖（interval graphs）、適當區間圖（proper interval graphs）、共圖（cographs）、和弦圖（chordal graphs）以及強弦圖（strongly chordal graphs）。文本最後研究了不同凸性類型下凸性參數的計算，包括在博弈論（game theory）等領域的實際應用。

本書內容簡潔明瞭，適合作為有意在凸性領域進一步研究的學生和研究人員的理想入門書籍。

本書的英文翻譯最初是由葡萄牙語翻譯而來，並由人工智慧協助完成。內容後來經作者修訂以確保準確性。

作者簡介

Júlio Araújo is a Professor at the Federal University of Ceará, Brazil. He holds a Master's degree (2009) and a PhD (2012) in Computer Science from the same University, with post-doc studies at the Centre de Recherche INRIA Sophia Antipolis and the Laboratoire d'Informatique, Robotique et Microélectronique de Montpellier, both in France.

Mitre C. Dourado is an Associate Professor at the Federal University of Rio de Janeiro, Brazil. He did his Master's (2001) and PhD (2005) studies at the same University and did post-doc studies at the Université Paris 13 (Paris-Nord), France.

Fábio Protti is a Full Professor at the Fluminense Federal University, Brazil. He holds Master's (1993) and PhD (1998) degrees in Systems Engineering and Computing from the Federal University of Rio de Janeiro, Brazil.

Rudini M. Sampaio is a Full Professor at the Federal University of Ceará, Brazil. He holds a Master's degree (2000) from the same university and a PhD (2008) from the University of São Paulo.

作者簡介(中文翻譯)

朱利奧·阿勞霍是巴西塞阿拉聯邦大學的教授。他於同一所大學獲得計算機科學碩士學位（2009年）和博士學位（2012年），並在法國的INRIA索非亞安提波利斯研究中心和蒙彼利埃計算機、機器人與微電子實驗室進行博士後研究。

米特雷·C·杜拉多是巴西里約熱內盧聯邦大學的副教授。他在同一所大學完成碩士學位（2001年）和博士學位（2005年），並在法國巴黎第十三大學（巴黎北）進行博士後研究。

法比奧·普羅提是巴西弗盧美聯邦大學的正教授。他於巴西里約熱內盧聯邦大學獲得系統工程與計算碩士學位（1993年）和博士學位（1998年）。

魯迪尼·M·桑帕約是巴西塞阿拉聯邦大學的正教授。他於同一所大學獲得碩士學位（2000年）和聖保羅大學的博士學位（2008年）。

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