PPT-1 Graph Coloring and Applications

2 Overview Graph Coloring Basics Planar4color Graphs Applications Chordal Graphs New Register Allocation Technique 3 Basics Assignment of colors to certain objects in a graph subject to certain constraints. CS594 Graph Theory. Graph Coloring. Coloring – Assignment of labels to vertices. k-coloring – a coloring where . Proper k-coloring – k-coloring where vertices have different labels if they are adjacent. Lindsay Mullen. (Abstract) Algebra and Number Theory. Combinatorics. (Discrete Mathematics). Graph Theory. Graph Coloring. What is Graph Theory?. Branch . of . mathematics . concerned with networks of points connected by . Recap. Omer Tripp. Register Allocation. (via graph coloring). Taken from . The Register Allocation Problem. Rewrite . the . intermediate code. to . use fewer temporaries. than there are . machine registers. Lecture 12 – Code Generation. Eran. . Yahav. 1. Reference: Dragon 8. MCD 4.2.4. www.cs.technion.ac.il/~. yahave/tocs2011/compilers-lec12.pptx. 2. You are here. Executable . code. exe. Source. text . Hamid. . Alaei. (Vertex) Coloring of a graph . G = (V,E) . is a map function . c. . : V → C. C. : set of colors. for every edge . vw. ∈ E: c(v) ≠ c(w). .. chromatic number . χ(G). is the minimal number of colors needed in a coloring of . Bart M. P. Jansen. Joint work with Stefan . Kratsch. August 22. nd . 2011, Oslo. Vertex Coloring of Graphs. Given an undirected graph G and integer q, can we assign each vertex a color from {1, 2, …, q} such that adjacent vertices have different colors?. N-Queens. The object is to place queens on a chess board in such a way as no queen can capture another one in a single move. Recall that a queen can move horizontally, vertically, or diagonally an infinite distance. By,. . Venkateswara reddy. Tallapu reddy. Outline. What is Timetable problem..?. . Subdivisions. 1. Debajyoti . Mondal. . 2. Rahnuma . Islam . Nishat. 2. Sue . Whitesides. . 3. Md. . . Saidur. . Rahman. 1. University of Manitoba, Canada. 2. University of Victoria, Canada. March 2014 Graph Coloring 1 Graph Coloring prepared and Instructed by Shmuel Wimer Eng. Faculty, Bar-Ilan University Vertex Coloring March 2014 Graph Coloring 2 A -coloring of a graph is a labeling Data Structures and Algorithms. CSE 373 WI 19 - Kasey Champion. 1. Last Time. We described algorithms to find:. CSE 373 SP 18 - Kasey Champion. 2. An ordering of the vertices so all edges go from left to right. . Data Structures and Algorithms. CSE 373 19 . Sp. - Kasey Champion. 1. Administrivia. HW 7 Due Friday. Final exam review Wednesday 6/5 4-5:50. Final exam next Tuesday!. Double check all grades . Please fill out survey. Discrete Structures (CS 173). Madhusudan Parthasarathy, University of Illinois. 1. http://en.wikipedia.org/wiki/File:7_bridgesID.png. Last Lecture: Graphs. How to represent graphs?. What are the properties of a graph?. Uriel Feige. Weizmann Institute. Joint work with . Roee David. 1. 3-. c. o. l. o. r. i. n. g. 2. 3-. c. o. l. o. r. i. n. g. 3. NP-hard problems. 3-coloring is NP-hard:. f. or every polynomial time 3-coloring algorithm, there are (worst case) 3-colorable graphs on which it fails. .