|
|
| Line 1: |
Line 1: |
| {{Infobox scientist
| |
| | name = David Shmoys
| |
| | image =
| |
| | image_size =
| |
| | caption = David Shmoys
| |
| | birth_date =
| |
| | birth_place =
| |
| | death_date =
| |
| | death_place =
| |
| | residence =
| |
| | citizenship =
| |
| | nationality =
| |
| | ethnicity =
| |
| | field = [[Computer Science]], [[Computational complexity theory]]
| |
| | work_institution = [[Cornell]]
| |
| | alma_mater = [[Princeton University|Princeton]], <br>[[University of California, Berkeley]]
| |
| | doctoral_advisor = [[Eugene Lawler]]
| |
| | doctoral_students =
| |
| | known_for =
| |
| | author_abbreviation_bot =
| |
| | author_abbreviation_zoo =
| |
| | prizes =
| |
| | religion =
| |
| | footnotes =
| |
| }}
| |
| '''David Shmoys''' is a Professor in the [[Cornell University College of Engineering|School of Operations Research and Information Engineering]] and the [[Cornell University College of Arts and Sciences|Department of Computer Science]] at [[Cornell University]]. He obtained his Ph.D. from the [[University of California, Berkeley]] in 1984. His major focus has been in the design and [[analysis of algorithms]] for discrete optimization problems.
| |
|
| |
|
| In particular, his work has highlighted the role of [[linear programming]] in the design of [[approximation algorithms]] for [[NP-hard]] problems. He is known for his pioneering research on providing first constant factor performance guarantee for several scheduling and clustering problems including the k-center and k-median problems and the generalized assignment problem. [[Polynomial-time approximation scheme]]s that he developed for [[Scheduling (computing)|scheduling]] problems have found applications in many subsequent works. His current research includes stochastic [[Optimization (mathematics)|optimization]], computational sustainability and optimization techniques in computational biology. Shmoys is married to [[Éva Tardos]], who is a Jacob Gould Schurman Professor of Computer Science at Cornell University.
| |
|
| |
|
| ==Key contributions==
| | CMS provides the best platform to create websites that fulfill all the specifications of SEO. You may discover this probably the most time-consuming part of building a Word - Press MLM website. Wordpress Content management systems, being customer friendly, can be used extensively to write and manage websites and blogs. Word - Press also provides protection against spamming, as security is a measure issue. After activating, you will find their website link and get the activation code from their website. <br><br>Generally, for my private income-making market websites, I will thoroughly research and discover the leading 10 most worthwhile niches to venture into. If you are a positive thinker businessman then today you have to put your business online. Our Daily Deal Software plugin brings the simplicity of setting up a Word - Press blog to the daily deal space. So if you want to create blogs or have a website for your business or for personal reasons, you can take advantage of free Word - Press installation to get started. Word - Press makes it possible to successfully and manage your website. <br><br>Just ensure that you hire experienced Word - Press CMS developer who is experienced enough to perform the task of Word - Press customization to get optimum benefits of Word - Press CMS. It was also the very first year that the category of Martial Arts was included in the Parents - Connect nationwide online poll, allowing parents to vote for their favorite San Antonio Martial Arts Academy. Setting Up Your Business Online Using Free Wordpress Websites. Enough automated blog posts plus a system keeps you and your clients happy. For any web design and development assignment, this is definitely one of the key concerns, specifically for online retail outlets as well as e-commerce websites. <br><br>Numerous bloggers are utilizing Word - Press and with good reason. Find more information about Design To Wordpress here. If you beloved this article so you would like to get more info concerning [http://mmservice.dk/backup_plugin_534500 wordpress dropbox backup] kindly visit our web site. To do this, you should link your posts to other relevant posts that you've created. A whole lot worse, your site will likely be useless as well as your merchandise won't sell if no one has the endurance to wait for the web pages to load. The popularity of Word - Press has increased the demand for Word - Press themes and these themes sells like hot cake on the internet. <br><br>There is no denying that Magento is an ideal platform for building ecommerce websites, as it comes with an astounding number of options that can help your online business do extremely well. An ease of use which pertains to both internet site back-end and front-end users alike. By the time you get the Gallery Word - Press Themes, the first thing that you should know is on how to install it. Page speed is an important factor in ranking, especially with Google. Definitely when you wake up from the slumber, you can be sure that you will be lagging behind and getting on track would be a tall order. |
| Two of his key contributions are
| |
| | |
| # Constant factor approximation algorithm for the [[Generalized Assignment Problem]] and [[Unrelated Parallel Machine Scheduling]].
| |
| | |
| # Constant factor approximation algorithm for [[k-Medians]] and [[Facility location problem]].
| |
| | |
| These contributions are described briefly below:
| |
| | |
| ===Generalized Assignment Problem & Unrelated Parallel Machine Scheduling===
| |
| | |
| The paper
| |
| <ref name=MATHPROG93>
| |
| {{cite journal
| |
| |doi= 10.1007/BF01585178
| |
| |author= D.B. Shmoys and E. Tardos
| |
| |title=An approximation algorithm for the generalized assignment problem
| |
| |journal= Mathematical Programming A
| |
| |volume = 62
| |
| |issue =1
| |
| |pages =461–474
| |
| |year= 1993
| |
| |url=http://portal.acm.org/citation.cfm?id=195719}}
| |
| </ref>
| |
| is a joint work by David Shmoys and Eva Tardos.
| |
| | |
| The generalized assignment problem can be viewed as the following problem of scheduling unrelated parallel machine with costs.
| |
| Each of <math>n</math> independent jobs (denoted <math> J </math>) have to be processed by exactly one of <math> m </math> unrelated parallel machines (denoted <math> M </math>). Unrelated implies same job might take different amount of processing time on different machines. Job <math>j</math> takes <math> p_{i,j} </math> time units when processed by machine <math> i </math> and incurs a cost <math> c_{i,j} , i=1,2,..,m; j=1,2,..,n; n \geq m</math>. Given <math> C </math> and <math> T_i , i=1,2,..,m </math>, we wish to decide if there exists a schedule with total cost at most <math> C </math> such that for each machine <math> i </math> its load, the total processing time required for the jobs assigned to it is at most <math> T_i , i=1,2,..,m </math>. By scaling the processing times, we can assume, without loss of generality, that the machine load bounds satisfy <math> T_1=T_2=..=T_m=T</math>. ``In other words, generalized assignment problem is to find a schedule of minimum cost subject to the constraint that the makespan, that the maximum machine load is at most <math> T </math> ".
| |
| | |
| The work of Shmoys with [[Jan Karel Lenstra|Lenstra]] and Tardos cited here
| |
| <ref name=MATHPROG193>
| |
| {{cite journal
| |
| |doi= 10.1007/BF01585745
| |
| |author= [[Jan Karel Lenstra|J. K. Lenstra]], D. B. Shmoys and É. Tardos
| |
| |title=Approximation algorithms for scheduling unrelated parallel machines
| |
| |journal= Mathematical Programming: Series a and B
| |
| |volume = 62
| |
| |issue =1
| |
| |pages =259–271
| |
| |year= 1990
| |
| |url=http://portal.acm.org/citation.cfm?id=81019}}
| |
| </ref>
| |
| gives a 2 approximation algorithm for the unit cost case. The algorithm is based on a clever design of linear program using [[parametric pruning]] and then rounding an [[extreme point solution]] of the linear program deterministically. Algorithm for the
| |
| generalized assignment problem is based on a similar LP through parametric pruning and then using a new rounding technique on a carefully designed bipartite graph. We now state the LP formulation and briefly describe the rounding technique.
| |
| | |
| We guess the optimum value of makespan <math> T </math> and write the following LP. This technique is known as parametric pruning.
| |
| | |
| <math>LP(T)::\sum_{i=1}^{m} \sum_{j=1}^n c_{ij} x_{ij} \le C </math>;
| |
| ::<math> \sum_{i=1}^m x_{ij} = 1 \qquad j=1, \ldots, n</math>;
| |
| ::<math> \sum_{i=1}^m p_{ij}x_{ij} \leq T \qquad i=1, \ldots, m</math>;
| |
| ::<math> x_{ij} \geq 0 \qquad i=1, \ldots, m, \quad j=1, \ldots, n</math>;
| |
| ::<math> x_{ij}=0 \qquad \text{if} \qquad p_{ij} \geq T, \qquad i=1, \ldots, m, \quad j=1, \ldots, n</math>;
| |
| | |
| The obtained LP solution is then rounded to an integral solution as follows. A weighted bipartite graph
| |
| <math> G=(W \cup V, E)</math> is constructed. One side of the bipartite graph contains the job nodes, <math> W =\{w_j | j \in J\}</math>, and the other side contains several copies of each machine node, | |
| <math> V=\{v_{i,s} | i=1,2,..,m; s=1,2,..,k_i \}</math>, where <math> k_i=\lceil \sum_{j} x_{ij} \rceil</math>. To construct the edges to machine nodes corresponding to say machine <math> i </math>, first jobs are arranged in decreasing order of processing time <math> p_{ij} </math>. For simplicity, suppose, <math> p_{i1} \geq p_{i2} \geq \ldots \geq p_{in}</math>. Now find the minimum index <math> j_1 </math>, such that
| |
| <math> \sum_{i}^{j_1} x_{ij} \geq 1</math>. Include in <math> E </math> all the edges <math> (w_j,v_{i1}, j=1,2,..,j_1-1) </math> with nonzero <math> x_{ij} </math> and set their weights to <math>x'_{v_{i1}j}= x_{ij} </math>. Create the edge <math> (w_{j_1}, v_{i1}) </math> and set its weight to <math> x'_{v_{i1}j_1}=1-\sum_{i=1}^{j_1-1} x'_{v_{i1}j} </math>. This ensures that the total weight of the edges incident on the vertex <math> v_{i1} </math> is at most 1. If <math>x'_{v_{i1}j_1} < x_{ij_1}</math>, then create an edge <math>(w_{j_1}, v_{i2})</math> with weight <math> x'_{v_{i2}j_1}=x_{ij}-x'_{v_{i1}j_1} </math>. Continue with assigning edges to <math> v_{i2} </math> in a similar way.
| |
| | |
| In the bipartite graph thus created, each job node in <math> W </math> has a total edge weight of 1 incident on it, and each machine node in <math> V </math> has edges with total weight at most 1 incident on it. Thus the vector <math> x' </math> is an instance of a fractional matching on <math> G </math> and thus it can be rounded to obtain an integral matching of same cost.
| |
| | |
| Now considering the ordering of processing times of the jobs on the machines nodes during construction of <math> G </math> and using an easy charging argument, the following theorem can be proved:
| |
| | |
| '''Theorem:''' If <math>LP(T)</math> has a feasible solution then a schedule can be constructed with makespan
| |
| <math> T + max_{i,j} p_{i,j} </math> and cost <math> C </math>.
| |
| | |
| Since <math> max_{i,j} p_{i,j} \leq T </math>, a 2 approximation is obtained.
| |
| | |
| ===K-medians and Facility Location Problem===
| |
| | |
| The paper
| |
| <ref name=JCSS02>
| |
| {{cite journal
| |
| |author= Moses Charikar, Sudipto Guha, Eva Tardos and David B. Shmoys
| |
| |title=A Constant-Factor Approximation Algorithm for the k-Median Problem
| |
| |journal= J. Comput. Syst. Sci.
| |
| |volume = 65
| |
| |issue =1
| |
| |pages= 129
| |
| |year= 2002
| |
| |doi=10.1006/jcss.2002.1882}}
| |
| </ref>
| |
| is a joint work by [[Moses Charikar]], [[Sudipto Guha]], [[Éva Tardos]] and David Shmoys. They obtain a <math> 6 \frac{2}{3} </math> approximation to the metric [[k medians]] problem. This was the first paper to break the previously best known <math> O(\log{k}\ \log{\log{k}})</math> approximation.
| |
| | |
| Shmoys has also worked extensively on the [[facility location]] problem. His recent results include obtaining a <math> 3 </math> approximation algorithm for the capacitated facility location problem. The joint work with [[Fabian Chudak]],
| |
| <ref name=S99>
| |
| {{cite journal
| |
| |doi=10.1007/s10107-004-0524-9
| |
| |author=Fabian A. Chudak and David B. Shmoys
| |
| |title=Improved Approximation Algorithms for a Capacitated Facility Location Problem
| |
| |journal=Mathematical Programming: Series a and B archive
| |
| |volume=102
| |
| |issue=2
| |
| |year=2005
| |
| |pages=207–222
| |
| |url=http://portal.acm.org/citation.cfm?id=1047776 }}
| |
| </ref>
| |
| has resulted in improving the previous known <math> 5.69 </math> approximation for the same problem. Their algorithm is based on a variant of [[randomized rounding]] called the randomized rounding with a backup, since a backup solution is incorporated to correct for the fact that the ordinary randomized rounding rarely generates a feasible solution to the associated [[set cover]]ing problem.
| |
| | |
| For the uncapacitated version of the facility location problem, again in a joint work with Chudak
| |
| <ref name=S03>
| |
| {{cite journal
| |
| |author=Fabian A. Chudak and David B. Shmoys
| |
| |title=Improved Approximation Algorithms for the Uncapacitated Facility Location Problem
| |
| |journal=SIAM J. Comput.
| |
| |volume=33
| |
| |issue=1
| |
| |year=2003
| |
| |url=http://epubs.siam.org/sam-bin/dbq/article/40575}}
| |
| </ref>
| |
| he obtained a <math> (1+2/e) \approx 1.736 </math>-approximation algorithm which was a significant improvement on the previously known approximation guarantees.
| |
| The improved algorithm works by rounding an optimal fractional solution of a linear programming relaxation and using the properties of the optimal solutions of the linear program and a generalization of a decomposition technique.
| |
| | |
| ==Awards & honors==
| |
| | |
| David Shmoys is an [[ACM Fellow]][http://fellows.acm.org/fellow_citation.cfm?id=2563864&srt=all]. He received College of Engineering Sonny Yau Excellence in Teaching Award three times and has been awarded NSF Presidential Young Investigator Award.
| |
| | |
| ==External links==
| |
| * {{MathGenealogy |id=36705}}
| |
| * [http://www.cs.cornell.edu/home/shmoys/shmoys.html David Shmoys's home page]
| |
| * [http://www.cs.cornell.edu/people/eva/eva.html Éva Tardos's home page]
| |
| | |
| ==References==
| |
| <references/>
| |
| | |
| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| |
| | NAME =Shmoys, David
| |
| | ALTERNATIVE NAMES =
| |
| | SHORT DESCRIPTION = American mathematician
| |
| | DATE OF BIRTH =
| |
| | PLACE OF BIRTH =
| |
| | DATE OF DEATH =
| |
| | PLACE OF DEATH =
| |
| }}
| |
| {{DEFAULTSORT:Shmoys, David}}
| |
| [[Category:Living people]]
| |
| [[Category:Cornell University faculty]]
| |
| [[Category:American mathematicians]]
| |
| [[Category:Theoretical computer scientists]]
| |
CMS provides the best platform to create websites that fulfill all the specifications of SEO. You may discover this probably the most time-consuming part of building a Word - Press MLM website. Wordpress Content management systems, being customer friendly, can be used extensively to write and manage websites and blogs. Word - Press also provides protection against spamming, as security is a measure issue. After activating, you will find their website link and get the activation code from their website.
Generally, for my private income-making market websites, I will thoroughly research and discover the leading 10 most worthwhile niches to venture into. If you are a positive thinker businessman then today you have to put your business online. Our Daily Deal Software plugin brings the simplicity of setting up a Word - Press blog to the daily deal space. So if you want to create blogs or have a website for your business or for personal reasons, you can take advantage of free Word - Press installation to get started. Word - Press makes it possible to successfully and manage your website.
Just ensure that you hire experienced Word - Press CMS developer who is experienced enough to perform the task of Word - Press customization to get optimum benefits of Word - Press CMS. It was also the very first year that the category of Martial Arts was included in the Parents - Connect nationwide online poll, allowing parents to vote for their favorite San Antonio Martial Arts Academy. Setting Up Your Business Online Using Free Wordpress Websites. Enough automated blog posts plus a system keeps you and your clients happy. For any web design and development assignment, this is definitely one of the key concerns, specifically for online retail outlets as well as e-commerce websites.
Numerous bloggers are utilizing Word - Press and with good reason. Find more information about Design To Wordpress here. If you beloved this article so you would like to get more info concerning wordpress dropbox backup kindly visit our web site. To do this, you should link your posts to other relevant posts that you've created. A whole lot worse, your site will likely be useless as well as your merchandise won't sell if no one has the endurance to wait for the web pages to load. The popularity of Word - Press has increased the demand for Word - Press themes and these themes sells like hot cake on the internet.
There is no denying that Magento is an ideal platform for building ecommerce websites, as it comes with an astounding number of options that can help your online business do extremely well. An ease of use which pertains to both internet site back-end and front-end users alike. By the time you get the Gallery Word - Press Themes, the first thing that you should know is on how to install it. Page speed is an important factor in ranking, especially with Google. Definitely when you wake up from the slumber, you can be sure that you will be lagging behind and getting on track would be a tall order.