CSE550 Combinatorial Algorithms/Intractability: Difference between revisions
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::-Theorem 1.2 (Kumar and Li, 2002) Any asymmetric TSP on n locations can be reducedto a symmetric TSP on 2n locations | ::-Theorem 1.2 (Kumar and Li, 2002) Any asymmetric TSP on n locations can be reducedto a symmetric TSP on 2n locations | ||
:*[http://www.sciencedirect.com.ezproxy1.lib.asu.edu/science?_ob=ArticleListURL&_method=list&_ArticleListID=654442605&_sort=d&view=c&_acct=C000059542&_version=1&_urlVersion=0&_userid=56861&md5=7c0e2798e0ed6ae5bd0b5865eea21691 Science Direct "Problems"] | :*[http://www.sciencedirect.com.ezproxy1.lib.asu.edu/science?_ob=ArticleListURL&_method=list&_ArticleListID=654442605&_sort=d&view=c&_acct=C000059542&_version=1&_urlVersion=0&_userid=56861&md5=7c0e2798e0ed6ae5bd0b5865eea21691 Science Direct "Problems"] | ||
== Midterm == | == Midterm == | ||
=== Q1 === | === Q1 === | ||
| Line 32: | Line 33: | ||
=== Q4 === | === Q4 === | ||
*[http://agecon2.tamu.edu/people/faculty/mccarl-bruce/mccspr/new04.pdf LP Primal Dual Tutorial] ? | *[http://agecon2.tamu.edu/people/faculty/mccarl-bruce/mccspr/new04.pdf LP Primal Dual Tutorial] ? | ||
== Final == | |||
=== Q2 === | |||
*[http://people.brunel.ac.uk/~mastjjb/jeb/or/netflow.html Minimum Cost Flow (Linear Programming)] | |||
== Project == | == Project == | ||
Revision as of 15:59, 29 November 2007
Resources
- -Unimodularity ensures that the solution to an LP will always be integer if all of the costs and constraints are also integer
- Linear Programming animation (simplex method)
- List of LP solvers (including NEOS)
- Integer Linear Programming Tutorial
- Interger Linear Programming Tutorial (CMU)
- Opensource Algorithm Code, Zuse Institute
- Lectures from the University of Freiburg
- > List of NP-Hard problems
HW 6
- 1. 2-SAT is in NP
- 2. A sub-optimal solution to TSP is a Hamiltonian Cycle.
- 3. 3SAT reduction to NAESAT
- 4. Finding disjoint paths with different path-costs: Complexity and algorithms
- Randeep Bhatia · Murali Kodialam · T. V. Lakshman, "Finding disjoint paths with related path costs", Springer Science+Business Media, LLC 2006
HW 7
- 1.
- Optimization Theory By Hubertus Th. Jongen, Klaus Meer, Eberhard Triesch, partial search result on Google book search
- Solution to part (a),(b)
- Solution to part (a),(b)
- Additional infor (a),(b), possible references for (c)
- -Theorem 1.2 (Kumar and Li, 2002) Any asymmetric TSP on n locations can be reducedto a symmetric TSP on 2n locations
Midterm
Q1
- Bin Zhang, Julie Ward, Qi Feng, "Simultaneous Parametric Maximum Flow Algorithm with Vertex Balancing", HP Laboratories Palo Alto, June 28, 2005
- J. M. W. Rhys, "A Selection Problem of Shared Fixed Costs and Network Flows", Management Science, Vol. 17, No. 3, Theory Series (Nov., 1970), pp. 200-207
Q4
Final
Q2
Project
2. Linear program formulation and solving. You can examine one or more linear programming formulations for a speci�c problem. This should be done by using a free solver, such as GLPK and a modeling language such as AMPL or the subset of AMPL that comes with GLPK. (If you have access to CPLEX and/or real AMPL, that is also perfectly fine with me.) Your goal in this might be to examine and compare the solution times for several formulations of a problem (as in the mincut example), or to study the tightness of a relaxation (as in the case of Steiner trees and edge coloring). Some suggestions for this type of project:
- -Comparing minimum cut formulations (standard cut covering, polynomial-size directed flow formulation, compact formulation by Carr et al.).
- -Bidirected formulation for the Steiner tree problem (Rajagopalan-Vazirani).
- -Asymmetric TSP (Charikar, Goemans, Karloff).
- -Matching-based LP relaxation of edge-coloring gap should be an additive 1! There is a paper by Jeff Kahn, but it is somewhat difficult.
- GNU Linear Programming Kit guide from IBM
- GLPsol Tutorial
- Practical Optimization: A Gentle Introduction
- Robert Fourer, AMPL: "A Mathematical Programming Language"
- LP formulations (covering, packing, partition) (non-linear information)
- Dan Bienstock, "Some Generalized Max-Flow Min-Cut Problems in the Plane" Mathematics of Operations Research, Vol. 16, No. 2. (May, 1991), pp. 310-333.
- Linear Programming and set covering problems (based on notes from Tardos)
