Computational problems in graph theory

Mixed Chinese postman problem

The mixed Chinese postman problem (MCPP or MCP) is the search for the shortest traversal of a graph with a set of vertices V, a set of undirected edges E with positive rational weights, and a set of directed arcs A with positive rational weights that covers each edge or arc at least once at minimal cost. The problem has been proven to be NP-complete by Papadimitriou. The mixed Chinese postman problem often arises in arc routing problems such as snow ploughing, where some streets are too narrow to traverse in both directions while other streets are bidirectional and can be plowed in both directions. This article assumes , which relates the computational complexity class of polynomial time with deterministic time to the set of NP complete problems. It is easy to check if a mixed graph has a postman tour of any size is easy to check by verifying if the graph is strongly connected. The problem is NP hard if we restrict the postman tour to traverse each arc exactly once or if we restrict it to traverse each edge exactly once, as proved by Zaragoza Martinez. (Wikipedia).

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The Story of Chinese Character : 介

介 depicts a man standing between two walls, which has the meaning of ‘between’.

From playlist The Story of HanZi (Chinese Characters)

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The Story of Chinese Character :攵

攵 depicts a hand holding a stick or tool, it is the variant of攴. 攴* is no longer an independent HanZi, it only exists as a BusShou or affix of the other HanZis such as牧and收. 攵 shares the same pronunciation and meaning as攴 and 扑.

From playlist The Story of HanZi (Chinese Characters)

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The Story of Chinese Character :束

束 depicts a package which its two end was tied by ropes. On the other hand, please be noted that 束 and 東(mean east) came from the same origin.

From playlist The Story of HanZi (Chinese Characters)

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The Chinese Postman Problem (Introduction to Graph Theory)

This video covers Eulerian, Semi-Eulerian, and regular graphs in the Chinese Postman Problem as well as applications of graph theory. This was made for 3Blue1Brown's Summer of Math Exploration video competition (link: https://www.3blue1brown.com/blog/some1). For more information about Eu

From playlist Summer of Math Exposition Youtube Videos

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The Story of Chinese Character : 畍

畍 is composed of 田(field) and 介, 介 depicts a man standing between two walls, which has the meaning of ‘between’, border or boundary lies between two fields. 畍 is the variant form of 界, both shares the same meaning and pronunciation.

From playlist The Story of HanZi (Chinese Characters)

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Chinese Postman Problem (Tutorial 11) D1 EDEXCEL A-Level

Powered by https://www.numerise.com/ This video is a tutorial on the Chinese Postman Problem or Route Inspection Problem for Decision 1 Math A-Level. Please make yourself revision notes while watching this and attempt my examples. Complete the suggested exercises from the Edexcel book.

From playlist Decision 1: Edexcel A-Level Maths Full Course

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The Story of Chinese Character :竝

竝 is composed of two 立, depicts two standing men, but 竝 is barely used nowadays and 並 is being used instead. Remarks: Although 並, 并 and竝 are different in their forms, their origins, pronunciations and meanings are the same.

From playlist The Story of HanZi (Chinese Characters)

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Chinese Postman problem / Route Inspection Problem (Decision Maths 1)

Powered by https://www.numerise.com/ Chinese Postman problem / Route Inspection Problem www.hegartymaths.com http://www.hegartymaths.com/

From playlist Decision Maths 1 OCR Exam Board (A-Level tutorials)

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AQA Decision 1 7.01 Introducing the Chinese Postman Algorithm

I introduce the Chinese Postman algorithm and give an example of how it works for a simple graph.

From playlist [OLD SPEC] TEACHING AQA DECISION 1 (D1)

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AQA Decision 1 7.03 Chinese Postman Algorithm: a third example w/extras

I work through a third example of using the Chinese Postman algorithm and throw in a couple of extra part (b) and (c) questions at the end.

From playlist [OLD SPEC] TEACHING AQA DECISION 1 (D1)

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The Story of Chinese Character : 界

界 is composed of 田(field) and 介, 介 depicts a man standing between two walls, which has the meaning of ‘between’, border or boundary lies between two fields. 界 is the variant form of 畍, both shares the same meaning and pronunciation.

From playlist The Story of HanZi (Chinese Characters)

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Lecture 25 - Project Presentations

This is Lecture 25 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2025.pdf More information may

From playlist CSE547 - Discrete Mathematics - 1999 SBU

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The Story of Chinese Character :并

并 depicts two people standing together. Remarks: Although 並, 并 and竝 are different in their forms, their origins, pronunciations and meanings are the same.

From playlist The Story of HanZi (Chinese Characters)

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The Story of Chinese Character: 並

並 depicts two people standing together. Remarks: Although 並, 并 and竝 are different in their forms, their origins, pronunciations and meanings are the same.

From playlist The Story of HanZi (Chinese Characters)

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Decision 1 Edexcel Maths A-Level January 2013 Q5

Powered by https://www.numerise.com/ Decision 1 Edexcel Maths A-Level January 2013 Q5 www.hegartymaths.com http://www.hegartymaths.com/

From playlist Decision 1 Maths A-Level Edexcel January 2013 Exam Paper

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The Story of Chinese Character :丞

丞 depicts two hands lifting a man who is falling in a hole. 丞 has the meaning of rescue, but such meaning has been replaced by 拯, now 丞 only means assistance.

From playlist The Story of HanZi (Chinese Characters)

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The Story of Chinese Character :禾

禾 depicts a piece of ripe paddy with a ear of grain on the top of it. 禾 is one of the radicals in HanZi.

From playlist The Story of HanZi (Chinese Characters)

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Travelling salesperson problem (Decision Maths 1)

Powered by https://www.numerise.com/ Travelling salesperson problem (Decision Maths 1). A video showing how to calculate an upper bound and lower bound as well as the nearest neighbour solution. Finally I finish off by showing how to use the tour improvement algorithm to attempt to find

From playlist Decision Maths 1 OCR Exam Board (A-Level tutorials)

Related pages

Capacitated arc routing problem | Strongly connected component | Time complexity | NP (complexity)