| Hits ?▲ |
Authors |
Title |
Venue |
Year |
Link |
Author keywords |
| 1 | Chandra Chekuri, Nitish Korula |
Pruning 2-Connected Graphs.  |
Algorithmica  |
2012 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sreeram Kannan, Adnan Raja, Pramod Viswanath |
Multicommodity flows and cuts in polymatroidal networks.  |
ITCS  |
2012 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Guy Even, Anupam Gupta, Danny Segev |
Set connectivity problems in undirected graphs and the directed steiner network problem.  |
ACM Transactions on Algorithms  |
2011 |
DBLP DOI BibTeX RDF |
|
| 1 | Spyridon Antonakopoulos, Chandra Chekuri, F. Bruce Shepherd, Lisa Zhang |
Buy-at-Bulk Network Design with Protection.  |
Math. Oper. Res.  |
2011 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Alina Ene |
Submodular Cost Allocation Problem and Applications  |
CoRR  |
2011 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, Jan Vondrák, Rico Zenklusen |
Submodular Function Maximization via the Multilinear Relaxation and Contention Resolution Schemes  |
CoRR  |
2011 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, Alina Ene |
Approximation Algorithms for Submodular Multiway Partition  |
CoRR  |
2011 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, Sreeram Kannan, Adnan Raja, Pramod Viswanath |
Multicommodity Flows and Cuts in Polymatroidal Networks  |
CoRR  |
2011 |
DBLP BibTeX RDF |
|
| 1 | Gruia Calinescu, Chandra Chekuri, Martin Pál, Jan Vondrák |
Maximizing a Monotone Submodular Function Subject to a Matroid Constraint.  |
SIAM J. Comput.  |
2011 |
DBLP DOI BibTeX RDF |
|
| 1 | MohammadHossein Bateni, Chandra Chekuri, Alina Ene, Mohammad Taghi Hajiaghayi, Nitish Korula, Dániel Marx |
Prize-collecting Steiner Problems on Planar Graphs.  |
SODA  |
2011 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, Jan Vondrák, Rico Zenklusen |
Multi-budgeted Matchings and Matroid Intersection via Dependent Rounding.  |
SODA  |
2011 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, Alina Ene |
Submodular Cost Allocation Problem and Applications.  |
ICALP  |
2011 |
DBLP DOI BibTeX RDF |
|
| 1 | Deeparnab Chakrabarty, Chandra Chekuri, Sanjeev Khanna, Nitish Korula |
Approximability of Capacitated Network Design.  |
IPCO  |
2011 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Alina Ene |
Approximation Algorithms for Submodular Multiway Partition.  |
FOCS  |
2011 |
DBLP DOI BibTeX RDF |
|
| 1 | Jan Vondrák, Chandra Chekuri, Rico Zenklusen |
Submodular function maximization via the multilinear relaxation and contention resolution schemes.  |
STOC  |
2011 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Alina Ene, Nitish Korula |
Prize-Collecting Steiner Tree and Forest in Planar Graphs  |
CoRR  |
2010 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, F. Bruce Shepherd, Christophe Weibel |
Flow-Cut Gaps for Integer and Fractional Multiflows  |
CoRR  |
2010 |
DBLP BibTeX RDF |
|
| 1 | Deeparnab Chakrabarty, Chandra Chekuri, Sanjeev Khanna, Nitish Korula |
Approximability of Capacitated Network Design  |
CoRR  |
2010 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, Mohammad Taghi Hajiaghayi, Guy Kortsarz, Mohammad R. Salavatipour |
Approximation Algorithms for Nonuniform Buy-at-Bulk Network Design.  |
SIAM J. Comput.  |
2010 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, F. Bruce Shepherd, Christophe Weibel |
Flow-Cut Gaps for Integer and Fractional Multiflows.  |
SODA  |
2010 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, Avigdor Gal, Sungjin Im, Samir Khuller, Jian Li, Richard Matthew McCutchen, Benjamin Moseley, Louiqa Raschid |
New Models and Algorithms for Throughput Maximization in Broadcast Scheduling - (Extended Abstract).  |
WAOA  |
2010 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Jan Vondrák, Rico Zenklusen |
Dependent Randomized Rounding via Exchange Properties of Combinatorial Structures.  |
FOCS  |
2010 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sanjeev Khanna, F. Bruce Shepherd |
A Note on Multiflows and Treewidth.  |
Algorithmica  |
2009 |
DBLP DOI BibTeX RDF |
Product multicommodity flow, Treewidth, Edge-disjoint paths |
| 1 | Chandra Chekuri, Luca Trevisan |
Foreword.  |
Algorithmica  |
2009 |
DBLP DOI BibTeX RDF |
|
| 1 | Gruia Calinescu, Chandra Chekuri, Jan Vondrák |
Disjoint bases in a polymatroid.  |
Random Struct. Algorithms  |
2009 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Jan Vondrák |
Randomized Pipage Rounding for Matroid Polytopes and Applications  |
CoRR  |
2009 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, Kenneth L. Clarkson, Sariel Har-Peled |
On the Set Multi-Cover Problem in Geometric Settings  |
CoRR  |
2009 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, Nitish Korula |
A Graph Reduction Step Preserving Element-Connectivity and Applications  |
CoRR  |
2009 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, Sungjin Im, Benjamin Moseley |
Minimizing Maximum Response Time and Delay Factor in Broadcast Scheduling  |
CoRR  |
2009 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, Iftah Gamzu |
Truthful Mechanisms via Greedy Iterative Packing  |
CoRR  |
2009 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, Sungjin Im, Benjamin Moseley |
Longest Wait First for Broadcast Scheduling  |
CoRR  |
2009 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, Sanjeev Khanna, F. Bruce Shepherd |
Edge-Disjoint Paths in Planar Graphs with Constant Congestion.  |
SIAM J. Comput.  |
2009 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sungjin Im, Benjamin Moseley |
Minimizing Maximum Response Time and Delay Factor in Broadcast Scheduling.  |
ESA  |
2009 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Benjamin Moseley |
Online scheduling to minimize the maximum delay factor.  |
SODA  |
2009 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Nitish Korula |
A Graph Reduction Step Preserving Element-Connectivity and Applications.  |
ICALP  |
2009 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Kenneth L. Clarkson, Sariel Har-Peled |
On the set multi-cover problem in geometric settings.  |
Symposium on Computational Geometry  |
2009 |
DBLP DOI BibTeX RDF |
set cover, cuttings, LP rounding |
| 1 | Chun-cheng Chen, Chandra Chekuri, D. Klabjan |
Topology Formation for Wireless Mesh Network Planning.  |
INFOCOM  |
2009 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sungjin Im, Benjamin Moseley |
Longest Wait First for Broadcast Scheduling [Extended Abstract].  |
WAOA  |
2009 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Alina Ene, Nitish Korula |
Unsplittable Flow in Paths and Trees and Column-Restricted Packing Integer Programs.  |
APPROX-RANDOM  |
2009 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Iftah Gamzu |
Truthful Mechanisms via Greedy Iterative Packing.  |
APPROX-RANDOM  |
2009 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Benjamin Moseley |
Online Scheduling to Minimize the Maximum Delay Factor  |
CoRR  |
2008 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, Nitish Korula |
Min-Cost 2-Connected Subgraphs With k Terminals  |
CoRR  |
2008 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, F. Bruce Shepherd |
Approximate Integer Decompositions for Undirected Network Design Problems.  |
SIAM J. Discrete Math.  |
2008 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri |
Multicommodity Flow, Well-linked Terminals and Routing Problems.  |
Encyclopedia of Algorithms  |
2008 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Guy Even, Anupam Gupta, Danny Segev |
Set connectivity problems in undirected graphs and the directed Steiner network problem.  |
SODA  |
2008 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Nitish Korula, Martin Pál |
Improved algorithms for orienteering and related problems.  |
SODA  |
2008 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sanjeev Khanna |
Algorithms for 2-Route Cut Problems.  |
ICALP  |
2008 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Nitish Korula |
Single-Sink Network Design with Vertex Connectivity Requirements.  |
FSTTCS  |
2008 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Nitish Korula |
Pruning 2-Connected Graphs.  |
FSTTCS  |
2008 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, F. Bruce Shepherd, Gianpaolo Oriolo, Maria Grazia Scutellà |
Hardness of robust network design.  |
Networks  |
2007 |
DBLP DOI BibTeX RDF |
|
| 1 | Amit Chakrabarti, Chandra Chekuri, Anupam Gupta, Amit Kumar |
Approximation Algorithms for the Unsplittable Flow Problem.  |
Algorithmica  |
2007 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Martin Pál |
An O(log n) Approximation Ratio for the Asymmetric Traveling Salesman Path Problem.  |
Theory of Computing  |
2007 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sanjeev Khanna |
Edge-disjoint paths revisited.  |
ACM Transactions on Algorithms  |
2007 |
DBLP DOI BibTeX RDF |
multicommodity flow relaxation, approximation algorithm, greedy algorithm, Edge-disjoint paths |
| 1 | Chandra Chekuri, Marcelo Mydlarz, F. Bruce Shepherd |
Multicommodity demand flow in a tree and packing integer programs.  |
ACM Transactions on Algorithms  |
2007 |
DBLP DOI BibTeX RDF |
Integer multicommodity flow, packing integer program, approximation algorithm, tree, integrality gap |
| 1 | Chandra Chekuri, Nitish Korula |
Approximation Algorithms for Orienteering with Time Windows  |
CoRR  |
2007 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri |
Routing and network design with robustness to changing or uncertain traffic demands.  |
SIGACT News  |
2007 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Julia Chuzhoy, Liane Lewin-Eytan, Joseph Naor, Ariel Orda |
Non-Cooperative Multicast and Facility Location Games.  |
IEEE Journal on Selected Areas in Communications  |
2007 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Mohammad Taghi Hajiaghayi, Guy Kortsarz, Mohammad R. Salavatipour |
Approximation algorithms for node-weighted buy-at-bulk network design.  |
SODA  |
2007 |
DBLP DOI BibTeX RDF |
|
| 1 | Gruia Calinescu, Chandra Chekuri, Martin Pál, Jan Vondrák |
Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract).  |
IPCO  |
2007 |
DBLP DOI BibTeX RDF |
|
| 1 | Spyridon Antonakopoulos, Chandra Chekuri, F. Bruce Shepherd, Lisa Zhang |
Buy-at-Bulk Network Design with Protection.  |
FOCS  |
2007 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sanjeev Khanna, F. Bruce Shepherd |
An O(sqrt(n)) Approximation and Integrality Gap for Disjoint Paths and Unsplittable Flow.  |
Theory of Computing  |
2006 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Paul Claisse, René-Jean Essiambre, Steven Fortune, Daniel C. Kilper, Wonsuck Lee, Nachi K. Nithi, Iraj Saniee, F. Bruce Shepherd, Christopher A. White, Gordon T. Wilfong, Lisa Zhang |
Design tools for transparent optical networks.  |
Bell Labs Technical Journal  |
2006 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Anupam Gupta, Ilan Newman, Yuri Rabinovich, Alistair Sinclair |
Embedding k-Outerplanar Graphs into l 1.  |
SIAM J. Discrete Math.  |
2006 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sudipto Guha, Joseph Naor |
The Steiner k-Cut Problem.  |
SIAM J. Discrete Math.  |
2006 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Guy Even, Guy Kortsarz |
A greedy approximation algorithm for the group Steiner problem.  |
Discrete Applied Mathematics  |
2006 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Daniele Micciancio |
Special Issue: FOCS 2003.  |
J. Comput. Syst. Sci.  |
2006 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Christina Fragouli, Emina Soljanin |
On average throughput and alphabet size in network coding.  |
IEEE Transactions on Information Theory  |
2006 |
DBLP DOI BibTeX RDF |
linear programming integrality gap, routing, multicast, throughput, network coding |
| 1 | Chandra Chekuri, Julia Chuzhoy, Liane Lewin-Eytan, Joseph Naor, Ariel Orda |
Non-cooperative multicast and facility location games.  |
ACM Conference on Electronic Commerce  |
2006 |
DBLP DOI BibTeX RDF |
multicast game, nash equilibrium, price of anarchy, price of stability |
| 1 | Chandra Chekuri, Martin Pál |
An O(logn) Approximation Ratio for the Asymmetric Traveling Salesman Path Problem.  |
APPROX-RANDOM  |
2006 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Mohammad Taghi Hajiaghayi, Guy Kortsarz, Mohammad R. Salavatipour |
Approximation Algorithms for Non-Uniform Buy-at-Bulk Network Design.  |
FOCS  |
2006 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sanjeev Khanna, F. Bruce Shepherd |
Edge-disjoint paths in Planar graphs with constant congestion.  |
STOC  |
2006 |
DBLP DOI BibTeX RDF |
Planar graphs, multicommodity flow, edge-disjoint paths |
| 1 | Chandra Chekuri, Anupam Gupta, Amit Kumar, Joseph Naor, Danny Raz |
Building Edge-Failure Resilient Networks.  |
Algorithmica  |
2005 |
DBLP DOI BibTeX RDF |
Backup path, Approximation algorithm, Network design, Restoration, Link failure |
| 1 | Chandra Chekuri, Anupam Gupta, Amit Kumar |
On a bidirected relaxation for the MULTIWAY CUT problem.  |
Discrete Applied Mathematics  |
2005 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sanjeev Khanna |
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem.  |
SIAM J. Comput.  |
2005 |
DBLP DOI BibTeX RDF |
|
| 1 | Li Li, Milind M. Buddhikot, Chandra Chekuri, Katherine Guo |
Routing bandwidth guaranteed paths with local restoration in label switched networks.  |
IEEE Journal on Selected Areas in Communications  |
2005 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Klaus Jansen, José D. P. Rolim, Luca Trevisan (eds.) |
Approximation, Randomization and Combinatorial Optimization, Algorithms and Techniques, 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and 9th InternationalWorkshop on Randomization and Computation, RANDOM 2005, Berkeley, CA, USA, August 22-24, 2005, Proceedings  |
APPROX-RANDOM  |
2005 |
DBLP BibTeX RDF |
|
| 1 | Moses Charikar, Chandra Chekuri, Martin Pál |
Sampling Bounds for Stochastic Optimization.  |
APPROX-RANDOM  |
2005 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Martin Pál |
A Recursive Greedy Algorithm for Walks in Directed Graphs.  |
FOCS  |
2005 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sanjeev Khanna, F. Bruce Shepherd |
Multicommodity flow, well-linked terminals, and routing problems.  |
STOC  |
2005 |
DBLP DOI BibTeX RDF |
all-or-nothing flow, flow-cut gaps, network routing, multicommodity flow, disjoint paths |
| 1 | Chandra Chekuri, Sanjeev Khanna, Joseph Naor, Leonid Zosin |
A Linear Programming Formulation and Approximation Algorithms for the Metric Labeling Problem.  |
SIAM J. Discrete Math.  |
2004 |
DBLP DOI BibTeX RDF |
|
| 1 | Moses Charikar, Chandra Chekuri, Tomás Feder, Rajeev Motwani |
Incremental Clustering and Dynamic Information Retrieval.  |
SIAM J. Comput.  |
2004 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sanjeev Khanna |
On Multidimensional Packing Problems.  |
SIAM J. Comput.  |
2004 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Amit Kumar |
Maximum Coverage Problem with Group Budget Constraints and Applications.  |
APPROX-RANDOM  |
2004 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sanjeev Khanna, F. Bruce Shepherd |
Edge-Disjoint Paths in Planar Graphs.  |
FOCS  |
2004 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Ashish Goel, Sanjeev Khanna, Amit Kumar |
Multi-processor scheduling to minimize flow time with epsilon resource augmentation.  |
STOC  |
2004 |
DBLP DOI BibTeX RDF |
multi-processor scheduling, load balancing, online algorithms, stretch, resource augmentation, flow time |
| 1 | Chandra Chekuri, Sanjeev Khanna, F. Bruce Shepherd |
The all-or-nothing multicommodity flow problem.  |
STOC  |
2004 |
DBLP DOI BibTeX RDF |
all-or-nothing multicommodity flow, approximation algorithms, online algorithms, multicommodity flow, oblivious routing, edge disjoint paths |
| 1 | Chandra Chekuri, Anupam Gupta, Ilan Newman, Yuri Rabinovich, Alistair Sinclair |
Embedding k-outerplanar graphs into l1.  |
SODA  |
2003 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sanjeev Khanna |
Edge disjoint paths revisited.  |
SODA  |
2003 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Marcelo Mydlarz, F. Bruce Shepherd |
Multicommodity Demand Flow in a Tree.  |
ICALP  |
2003 |
DBLP DOI BibTeX RDF |
integer multicommodity flow, packing integer program, approximation algorithm, tree, integrality gap |
| 1 | Chandra Chekuri, Sudipto Guha, Joseph Naor |
Approximating Steiner k-Cuts.  |
ICALP  |
2003 |
DBLP DOI BibTeX RDF |
Multiway Cut, $k$-Cut, Steiner tree, minimum cut, primal-dual |
| 1 | Erran L. Li, Milind M. Buddhikot, Chandra Chekuri, Katherine Guo |
Routing Bandwidth Guaranteed Paths with Local Restoration in Label Switched Networks. (PDF / PS)  |
ICNP  |
2002 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Anupam Gupta, Amit Kumar, Joseph Naor, Danny Raz |
Building Edge-Failure Resilient Networks.  |
IPCO  |
2002 |
DBLP BibTeX RDF |
|
| 1 | Amit Chakrabarti, Chandra Chekuri, Anupam Gupta, Amit Kumar |
Approximation Algorithms for the Unsplittable Flow Problem.  |
APPROX  |
2002 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sanjeev Khanna |
Approximation schemes for preemptive weighted flow time.  |
STOC  |
2002 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sanjeev Khanna |
Approximation Schemes for Preemptive Weighted Flow Time  |
Electronic Colloquium on Computational Complexity (ECCC)  |
2001 |
DBLP BibTeX RDF |
|
| 1 | Chandra Chekuri, Michael A. Bender |
An Efficient Approximation Algorithm for Minimizing Makespan on Uniformly Related Machines.  |
J. Algorithms  |
2001 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Rajeev Motwani, B. Natarajan, Clifford Stein |
Approximation Techniques for Average Completion Time Scheduling.  |
SIAM J. Comput.  |
2001 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sanjeev Khanna, Joseph Naor |
A deterministic algorithm for the cost-distance problem.  |
SODA  |
2001 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sanjeev Khanna, Joseph Naor, Leonid Zosin |
Approximation algorithms for the metric labeling problem via a new linear programming formulation.  |
SODA  |
2001 |
DBLP DOI BibTeX RDF |
|
| 1 | Chandra Chekuri, Sanjeev Khanna |
A PTAS for Minimizing Weighted Completion Time on Uniformly Related Machines.  |
ICALP  |
2001 |
DBLP DOI BibTeX RDF |
average completion time, uniformly related machines, weighted completion time, scheduling, Polynomial time approximation scheme |