Algorithms Seminar/Spring10

'''Topics in Graph Algorithms'''

'''Wed 3:40-5:00'''
'''MEB 3105'''



==Participants==
* [http://www.cs.utah.edu/~suresh Suresh Venkatasubramanian], Assistant Professor, School of Computing
* [http://www.cs.utah.edu/~jeffp Jeff Phillips], CI Postdoctoral Fellow, School of Computing
* [http://www.cs.utah.edu/~praman Parasaran Raman], PhD Student, School of Computing
* [mailto:rajvarma@cs.utah.edu Raj Varma Kommaraju], MS Student, School of Computing
* [mailto:avishek@cs.utah.edu Avishek Saha], PhD Student, School of Computing
* [mailto:moeller@cs.utah.edu John Moeller], PhD Student, School of Computing
* [mailto:jags@cs.utah.edu Jagadeesh Jagarlamudi], PhD Student, School of Computing
* [http://www.cs.utah.edu/~piyush Piyush Rai], PhD Student, School of Computing
* [http://www.cs.utah.edu/~huangrh Ruihong Huang], PhD Student, School of Computing
* [mailto:jiang@cs.utah.edu Jiarong Jiang], PhD Student, School of Computing
* [http://www.jtolds.com/ JT Olds], PhD Student, School of Computing
* [mailto:seth@cs.utah.edu Seth Juarez], PhD Student, School of Computing

==Schedule==
{|  border="1" style="width: 100%; text-align:left" class="content"
|-
! Date || Topic || Paper(s) || Presenter 
|-
| colspan="4" bgcolor="#dddddd" style = "text-align:center" | '''Planarity, Treewidth and Minors''' 
|-
| Jan 13 || Planar graphs and separators|| [http://infolab.stanford.edu/pub/cstr/reports/cs/tr/77/627/CS-TR-77-627.pdf Lipton-Tarjan separator theorem], [http://www-2.cs.cmu.edu/~glmiller/Publications/Papers/Mi87.pdf Gary Miller's cycle separator]|| Suresh [[Talk:Algorithms_Seminar/Spring10#Jan_13|(notes)]]
|-
| Jan 27 || Applications of Separators: The MIS problem || [ftp://reports.stanford.edu/pub/cstr/reports/cs/tr/77/628/CS-TR-77-628.pdf Lipton-Tarjan], [http://faculty.cs.tamu.edu/chen/courses/cpsc669/s2003/project/baker.pdf Baker]|| JT
|-
| Feb 3 || Treewidth: defns, results, applications|| [http://compgeom.cs.uiuc.edu/~jeffe/teaching/comptop/notes/treewidth.pdf Erickson notes]. Also read Shiva Kintali's recent [http://kintali.wordpress.com/2010/01/28/approximating-treewidth/ blog post]. [http://www.cs.uu.nl/research/techreps/repo/CS-1992/1992-27.pdf Bodlaender'96]|| Parasaran
|-
| Feb 10 || Minors. well-quasi orders, kruskal, wagner, robertson-seymour. || [http://en.wikipedia.org/wiki/Well-quasi-ordering well-quasi orders], [http://www.google.com/url?sa=t&source=web&ct=res&cd=15&ved=0CCAQFjAEOAo&url=ftp%3A%2F%2Fftp.cis.upenn.edu%2Fpub%2Fpapers%2Fgallier%2Fkruskal1.ps&ei=h6VQS5P2JYf8tQO44c32Bw&usg=AFQjCNHqsIMWSZrggRSBdOPHY-tH_QncsQ&sig2=X0fWrAhen16BpJo7nVRqww Higman's lemma (Section 3)], [http://en.wikipedia.org/wiki/Kruskal%27s_tree_theorem Kruskal's theorem], [http://compgeom.cs.uiuc.edu/~jeffe/teaching/comptop/notes/graph-minors.pdf Erickson notes]|| Suresh
|- 
| Feb 17 || Diameter-treewidth: graphs of bounded treewidth exclude planar graphs. bidimensionality.|| [http://www.cs.utah.edu/~suresh/seminar/spring10/diam-treewidth/notes.pdf My notes], [http://www.cs.utah.edu/~suresh/seminar/spring10/diam-treewidth/bidim-ptas.pdf Demaine/Hajighayi paper] on bidimensionality for approximations (only Section 4) || Ruihong
|-
| colspan="4" bgcolor="#dddddd" style = "text-align:center" | '''Spectral Graph Theory''' 
|-
| Feb 24 || Spectral properties of graphs: Laplacian and connectivity||Dan Spielman's lecture notes, [http://www.cs.yale.edu/homes/spielman/561/lect02-09.pdf part I] and [http://www.cs.yale.edu/homes/spielman/561/lect03-09.pdf part  II] || Jiarong
|- 
| Mar 3 || Second eigenvalue and cuts. Cheeger's inequality|| Dan Spielman's lecture notes ([http://www.cs.yale.edu/homes/spielman/561/lect05-09.pdf part I] (for the importance of the second eigenvalue of L, and [http://www.cs.yale.edu/homes/spielman/561/lect07-09.pdf part II], for Cheeger's inequality)|| Jags
|-
| Mar 10 || Separators via spectral properties|| [http://tcsmath.wordpress.com/2008/10/08/lecture-4-conformal-mappings-circle-packings-and-spectral-geometry/ James Lee outline], [http://www.cs.yale.edu/homes/spielman/course/lect3.ps Dan Spielman notes on Koebe theorem], [http://www.cs.washington.edu/homes/jrl/tocmath08/st.pdf main Spielman-Teng paper] (only the first four sections) || Seth
|-
| Mar 17 || Spectral Sparsification || [http://arxiv.org/PS_cache/arxiv/pdf/0803/0803.0929v4.pdf Srivastava/Spielman paper on spectral sparsification], [http://www.cs.yale.edu/homes/srivastava/papers/sparse-talk.pdf Nikhil Srivastava's slides] || John
|-
| colspan="4" bgcolor="#dddddd" style = "text-align:center" | '''Graph Algorithms''' 
|-
| Mar 31 || Planarity Testing  || [http://www.cs.brown.edu/~rt/gdhandbook/chapters/planarity.pdf Planarity Testing and Embedding notes], [http://portal.acm.org/citation.cfm?id=321852 The seminal Hopcroft-Tarjan paper], State-of-the-art: [http://jgaa.info/accepted/2004/BoyerMyrvold2004.8.3.pdf Simplified O(n) Planarity by Edge Addition] and [http://hal.archives-ouvertes.fr/docs/00/09/78/36/PDF/Planarity0.pdf Tremaux trees and planarity] || Piyush
|-
| Apr 7 || Randomized linear time MST || [http://www.cs.jhu.edu/~jason/papers/eisner.mst-tutorial.pdf Section 7 in this paper], and [http://www.cs.brown.edu/research/pubs/pdfs/1995/Karger-1995-RLT.pdf the original Karger/Klein/Tarjan paper] ||   Raj
|-
| Apr <strike>14</strike> 16 (in Graphics Annex) || Shortest Paths ||  [http://reference.kfupm.edu.sa/content/o/n/on_the_all_pairs_shortest_path_problem_59456.pdf On the all-pairs shortest path problem]|| JT
|- 
| Apr <strike>21</strike> '''23 (in LCR)''' || Dynamic Graph Algorithms || [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.8372 Survey] (focus on the min spanning forest problem - parts of Sec 4 and 5) and sparsification) || Brian M
|-
| colspan="4" bgcolor="#dddddd" style = "text-align:center" | '''Evasiveness: Graphs meet topology''' 
|-
| Apr 28 || || ||
|-
| May 5? || ||  ||
|}

== Reading Dumplist ==
* [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V1G-40M56FP-7&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=9baa28dec88cdd8542eed9fc9613b8d3 On computing graph minor obstruction sets]
* [http://www2.informatik.hu-berlin.de/~grohe/pub/gro03b.pdf Local treewidth and approximations]
* [http://e-math1.ams.org/bull/2006-43-01/S0273-0979-05-01088-8/S0273-0979-05-01088-8.pdf Lovasz review of graph minor theory]
* [http://www.cs.jhu.edu/~jason/papers/eisner.mst-tutorial.pdf MST survey]


* separator structures on graphs: planarity, treewidth, and the robertson-seymour theorem
** [http://infolab.stanford.edu/pub/cstr/reports/cs/tr/77/627/CS-TR-77-627.pdf Lipton-Tarjan separator theorem]
** [http://www-2.cs.cmu.edu/~glmiller/Publications/Papers/Mi87.pdf Gary Miller's cycle separator]
** An application: [http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.93.4667&rep=rep1&type=pdf linear time shortest paths for planar graphs]
** Application: [http://historical.ncstrl.org/litesite-data/stan/CS-TR-77-628.pdf PTAS for finding  maximum independent sets in planar graphs]

* [http://www.cs.uu.nl/research/techreps/repo/CS-1992/1992-12.pdf A tourist guide through treewidth]
** Application: [http://www.eecs.berkeley.edu/~wainwrig/Papers/WaiJor08_FTML.pdf junction trees in graphical models (2.5.2)]
** Application: solving NP-hard problems on graphs of bounded treewidth. 
** [http://archive.cs.uu.nl/pub/RUU/CS/techreps/CS-1997/1997-31.ps.gz General algorithmic methods for solving problems on graphs of bounded treewidth]
** [http://www.google.com/url?sa=t&source=web&ct=res&cd=24&ved=0CBkQFjADOBQ&url=http%3A%2F%2Fhomepages.ecs.vuw.ac.nz%2F~mathmeet%2Fnewplymouth%2Fnzm1.ps&ei=JDhES4CmJIn8tAOO6I0h&usg=AFQjCNFa4EbJPnSO4V8RTgJNexKe98rHQw&sig2=83aPogymDvnNN1QQA77I7w Nice survey of Courcelle's theorem and implications]. 
* [http://www.cs.tau.ac.il/~nogaa/PDFS/spr.pdf separators for graphs with excluded minors]
* Spectral properties of graphs
** laplacian and connectivity
** second eigenvalue and cuts. Cheeger's inequality
** [http://www.cs.yale.edu/homes/spielman/561/lect25-09.pdf Spielman/Teng spectral separator theorem] and [http://math.mit.edu/~spielman/course/lect3.html related notes]: 
** [http://arxiv.org/abs/0808.4134 spectral sparsification]
* evasiveness
** '''Hot off the presses''': [http://arxiv.org/abs/1001.4829 Evasiveness and the Distribution of Prime Numbers]