PPT-Data Reduction for Graph Coloring Problems

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. 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 . 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. 2. Overview. Graph Coloring Basics. Planar/4-color Graphs. Applications. Chordal Graphs. New Register Allocation Technique. 3. Basics. Assignment of . "colors". to certain objects in a . graph. subject to certain constraints. Theory of Computation. Alexander . Tsiatas. Spring 2012. Theory of Computation Lecture Slides by Alexander . Tsiatas. is licensed under a Creative Commons Attribution-. NonCommercial. -. ShareAlike. By,. . Venkateswara reddy. Tallapu reddy. Outline. What is Timetable problem..?. Proof Techniques and Chessboard Problems Graph Terms (informal) Independent Set : (packing, anti-clique): a set of nonadjacent vertices Dominating Set : (covering): a set of vertices that together are adjacent to all the other vertices. 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. 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. .