PDF-Using Dual Approximation Algorithms for Scheduling Problems Theoretical and Practical

HOCHBAUM University of California Berkeley Calijornia AND DAVID B SHMOYS Mussuchasetts Institute of Technology Cambridge Massachusetts Abstract The problem of scheduling a set of n jobs on m identical machines so as to minimize the makespan time is. HOCHBAUM AND WOLFGANG MAASS University of California Berkeley California Abstract A unified and powerful approach is presented for devising polynomial approximation schemes for many strongly NPcomplete problems Such schemes consist of families of ap Algorithms. and Networks 2014/2015. Hans L. . Bodlaender. Johan M. M. van Rooij. C-approximation. Optimization problem: output has a value that we want to . maximize . or . minimize. An algorithm A is an . 1) . M. Hajiaghayi, . Khandekar. and K.. 2) . M. . Cygan. ,. K. 3) . R . Chitnis. , . M. Hajiaghayi. ,. K . 4) . M. Hajiaghayi, K and some students of M. Hajiaghayi. Optimal running times for exact solutions and approximated solutions. Algorithms. and Networks 2015/2016. Hans L. . Bodlaender. Johan M. M. van Rooij. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. A. A. A. A. A. A. A. What to do if a problem is. Peter Andras. School of Computing and Mathematics. Keele University. p.andras@keele.ac.uk. Overview. High-dimensional functions and low-dimensional manifolds. Manifold mapping. Function approximation over low-dimensional projections. Anirudh . Sivaraman. , . Suvinay. Subramanian, . Anurag. Agrawal, . Sharad. . Chole. , Shang-. Tse. Chuang, Tom . Edsall. , Mohammad . Alizadeh. , . Sachin. . Katti. , Nick . McKeown. , . Hari. . Robert . Grandl. , University of Wisconsin—Madison; . Mosharaf. Chowdhury, University of Michigan; Aditya . Akella. , University of Wisconsin—Madison; Ganesh . Ananthanarayanan. , Microsoft. Proceedings of the 12th USENIX Symposium on Operating Systems Design and Implementation (OSDI ’16). Grigory. . Yaroslavtsev. . Penn State + AT&T Labs - Research (intern). Joint work with . Berman (PSU). , . Bhattacharyya (MIT). , . Makarychev. (IBM). , . Raskhodnikova. (PSU). Directed. Spanner Problem. Facilitators/Scribes: Gil . Zussman. (Columbia University), Justin Shi (Temple University) . Attendees: . Ioannis. . Stavrakakis. , Gustavo de . Veciana. , . Svetha. . Venkatesh. , Bill . Schilit. Problem - a well defined task.. Sort a list of numbers.. Find a particular item in a list.. Find a winning chess move.. Algorithms. A series of precise steps, known to stop eventually, that solve a problem.. Stochastic . Optimization. Anupam Gupta. Carnegie Mellon University. IPCO Summer . School. Approximation . Algorithms for. Multi-Stage Stochastic Optimization. {vertex cover, . S. teiner tree, MSTs}. EECT 7327 . Fall 2014. Successive Approximation. (SA) ADC. Successive Approximation ADC. – . 2. –. Data Converters Successive Approximation ADC Professor Y. Chiu. EECT 7327 . Fall 2014. Binary search algorithm → N*. When the best just isn’t possible. Jeff Chastine. Approximation Algorithms. Some NP-Complete problems are too important to ignore. Approaches:. If input small, run it anyway. Consider special cases that may run in polynomial time. Problem. What is it?. Implementation. Benefits. Experimentation. Findings. Other Scheduling Algorithms. Conclusion. . Outline. Problem. “Scheduling computations in multi-threaded systems is complex, and challenging problem.”.