Award Abstract # 1421231
AF: Small: Towards better geometric algorithms: Summarizing, partitioning and shrinking data

NSF Org: CCF
Division of Computing and Communication Foundations
Recipient: UNIVERSITY OF ILLINOIS
Initial Amendment Date: June 11, 2014
Latest Amendment Date: June 11, 2014
Award Number: 1421231
Award Instrument: Standard Grant
Program Manager: Joseph Maurice Rojas
CCF
 Division of Computing and Communication Foundations
CSE
 Directorate for Computer and Information Science and Engineering
Start Date: September 1, 2014
End Date: August 31, 2019 (Estimated)
Total Intended Award Amount: $490,364.00
Total Awarded Amount to Date: $490,364.00
Funds Obligated to Date: FY 2014 = $490,364.00
History of Investigator:
  • Sariel Har-Peled (Principal Investigator)
    sariel@uiuc.edu
Recipient Sponsored Research Office: University of Illinois at Urbana-Champaign
506 S WRIGHT ST
URBANA
IL  US  61801-3620
(217)333-2187
Sponsor Congressional District: 13
Primary Place of Performance: University of Illinois at Urbana-Champaign
1901 S. First Street
Champaign
IL  US  61820-7406
Primary Place of Performance
Congressional District:
13
Unique Entity Identifier (UEI): Y8CWNJRCNN91
Parent UEI: V2PHZ2CSCH63
NSF Program(s): Algorithmic Foundations
Primary Program Source: 01001415DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s): 7923, 7929
Program Element Code(s): 779600
Award Agency Code: 4900
Fund Agency Code: 4900
Assistance Listing Number(s): 47.070

ABSTRACT

New (and not so new) technologies like GPS, LIDAR, smart-phones and apps are now used to collect vast amounts of geometric and geographic data. In many such cases the data is too large to be handled by a single computer, and it needs to be broken up into small chunks, so that it can be handled by a cluster/cloud of computers. This award funds research to develop efficient algorithms for manipulating and summarizing such data. In particular, this award concentrates on the issue of how to partition such data efficiently in a balanced way, so that it can be efficiently processed.

The algorithms and insights obtained from the technical work will benefit Computer Science and related disciplines where geometric data and algorithms are widely used. The PI hopes to broaden the scope of Computer Science (and Computational Geometry) by introducing new techniques, that would lead to faster and better algorithms, and potentially new applications of geometric data.

The project will support and train at least two new PhD students in Computer Science at UIUC. The PI is committed to popularizing ideas and techniques that would be investigated by this proposal, by giving courses, publishing the research, potentially writing a new book on the topic, and use less convectional new tools to disseminate the research using blogs, social media, and online videos.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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(Showing: 1 - 10 of 25)
A. {Blum} and S. {Har-Peled} and B. {Raichel} "{Sparse Approximation via Generating Point Sets}" ArXiv e-prints , 2015
{Blum}, A. and {Har-Peled}, S. and {Raichel}, B. "{Sparse Approximation via Generating Point Sets}" ArXiv e-prints , 2015
Blum, Avrim and Har{-}Peled, Sariel and Raichel, Benjamin "Sparse Approximation via Generating Point Sets" ACM Trans. Algo. , v.15 , 2019 , p.32:1--32: 10.1145/3302249
Cheong, O. and Har{-}Peled, S. and Kim, H. and Kim, H. "On the Number of Edges of Fan-Crossing Free Graphs" Algorithmica , v.73 , 2015 , p.673--695 10.1007/s00453-014-9935-z
D. {Eppstein} and S. {Har-Peled} and A. {Sidiropoulos} "{Approximate Greedy Clustering and Distance Selection for Graph Metrics}" ArXiv e-prints , 2015
D. {Eppstein} and S. {Har-Peled} and A. {Sidiropoulos} "{Approximate Greedy Clustering and Distance Selection for Graph Metrics}" ArXiv e-prints , 2015
{Eppstein}, D. and {Har-Peled}, S. and {Sidiropoulos}, A. "{Approximate Greedy Clustering and Distance Selection for Graph Metrics}" ArXiv e-prints , 2015
{Har-Peled}, S. and {Quanrud}, K. "Approximation Algorithms for Low-Density Graphs" ArXiv e-prints , 2015
Har{-}Peled, Sariel "Shortest path in a polygon using sublinear space" J. Comput. Geom. , v.7 , 2016 , p.19--45 10.4230/LIPIcs.SOCG.2015.111
Har{-}Peled, Sariel and Jones, Mitchell "On Separating Points by Lines" CoRR , v.abs/170 , 2017
Har{-}Peled, Sariel and Kumar, Nirman "Robust Proximity Search for Balls Using Sublinear Space" Algorithmica , v.80 , 2018 , p.279--299 10.1007/s00453-016-0254-4
(Showing: 1 - 10 of 25)

PROJECT OUTCOMES REPORT

Disclaimer

This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.

This research project studied problems related to how to partition geometric data, and summarizing it.  Such tasks are fundamental tasks in real world applications, ranging from web search, machine learning, data-mining and others. They are of special importance when handling big data.

We developed new algorithms addressing issues such as (i) how to partition graphs that rises out of geometric data, (ii) how to find sparse representation of data, (iii) how to separate data using as few features as possible, (iv) how to perform certain geometric tasks using little space (important in handling big data), and (v) others.

This project had resulted in a significant progress of the state of the art algorithms for geometric problems using divide and conquer techniques. Highlights of this project includes: (i) the development of separators for low density graphs, and (ii) progress on computing sparse approximation of data in high dimensions.

Maybe the highlight of this project is a new technique, called locality sensitive orderings, which dramatically simplifies several geometric algorithms. We believe this technique has the potential to have a large impact in the long run.

Several graduate students were trained as part of this grant, one of them currently hold a faculty position in a US university. Another postdoc is currently holding a faculty in a university. The research done for this project resulted in the publication of 20 papers in prestigious conferences and journals.


Last Modified: 11/02/2019
Modified by: Sariel Har-Peled

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