Submodular optimization problems and greedy strategies: A survey

Liu, Yajing; Chong, Edwin K. P.; Pezeshki, Ali; Zhang, Zhenliang

doi:10.1007/s10626-019-00308-7

Title: Submodular optimization problems and greedy strategies: A survey

Abstract

The greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How effective is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two classes of optimization problems where the objective function is submodular. The first is set submodular optimization, which is to choose a set of actions to optimize a set submodular objective function, and the second is string submodular optimization, which is to choose an ordered set of actions to optimize a string submodular function. Our emphasis here is on performance bounds for the greedy strategy in submodular optimization problems. Specifically, we review performance bounds for the greedy strategy, more general and improved bounds in terms of curvature, performance bounds for the batched greedy strategy, and performance bounds for Nash equilibria.

Authors:

^[1]; Chong, Edwin K. P. ^[2]; Pezeshki, Ali ^[2]; Zhang, Zhenliang ^[3]

National Renewable Energy Lab. (NREL), Golden, CO (United States)
Colorado State Univ., Fort Collins, CO (United States)
Alibaba iDST, Seattle, WA (United States)

Publication Date:: Mon Feb 17 00:00:00 EST 2020

Research Org.:: National Renewable Energy Laboratory (NREL), Golden, CO (United States)

Sponsoring Org.:: USDOE Office of Energy Efficiency and Renewable Energy (EERE)

OSTI Identifier:: 1603264

Report Number(s):: NREL/JA-5D00-72380
Journal ID: ISSN 0924-6703; MainId:23579;UUID:e683f2b0-dbb5-e811-9c16-ac162d87dfe5;MainAdminID:12055

Grant/Contract Number:: AC36-08GO28308

Resource Type:: Accepted Manuscript

Journal Name:: Discrete Event Dynamic Systems

Additional Journal Information:: Journal Volume: 30; Journal Issue: 3; Journal ID: ISSN 0924-6703

Publisher:: Springer Nature

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; curvature; greedy strategy; Nash equilibrium; performance; optimization; submodular

Citation Formats


                    Liu, Yajing, Chong, Edwin K. P., Pezeshki, Ali, and Zhang, Zhenliang. Submodular optimization problems and greedy strategies: A survey.  United States: N. p., 2020. 
Web.  doi:10.1007/s10626-019-00308-7.

Copy to clipboard


                    Liu, Yajing, Chong, Edwin K. P., Pezeshki, Ali, & Zhang, Zhenliang. Submodular optimization problems and greedy strategies: A survey.  United States.  https://doi.org/10.1007/s10626-019-00308-7

Copy to clipboard


                    Liu, Yajing, Chong, Edwin K. P., Pezeshki, Ali, and Zhang, Zhenliang. Mon .  
"Submodular optimization problems and greedy strategies: A survey".  United States.  https://doi.org/10.1007/s10626-019-00308-7.  https://www.osti.gov/servlets/purl/1603264.

Copy to clipboard


                    
@article{osti_1603264,

  title        = {Submodular optimization problems and greedy strategies: A survey},

  author       = {Liu, Yajing and Chong, Edwin K. P. and Pezeshki, Ali and Zhang, Zhenliang},

  abstractNote = {The greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How effective is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two classes of optimization problems where the objective function is submodular. The first is set submodular optimization, which is to choose a set of actions to optimize a set submodular objective function, and the second is string submodular optimization, which is to choose an ordered set of actions to optimize a string submodular function. Our emphasis here is on performance bounds for the greedy strategy in submodular optimization problems. Specifically, we review performance bounds for the greedy strategy, more general and improved bounds in terms of curvature, performance bounds for the batched greedy strategy, and performance bounds for Nash equilibria.},

  doi          = {10.1007/s10626-019-00308-7},

  journal      = {Discrete Event Dynamic Systems},

  number       = 3,

  volume       = 30,

  place        = {United States},

  year         = {Mon Feb 17 00:00:00 EST 2020},

  month        = {Mon Feb 17 00:00:00 EST 2020}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1007/s10626-019-00308-7

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 5 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Optimization Strategies in Adaptive Control: A Selective Survey
journal, January 1975

Jarvis, R. A.
IEEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-5, Issue 1
DOI: 10.1109/TSMC.1975.5409158

Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
journal, January 2011

Calinescu, Gruia; Chekuri, Chandra; Pál, Martin
SIAM Journal on Computing, Vol. 40, Issue 6
DOI: 10.1137/080733991

Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms
journal, April 1977

Cornuejols, Gerard; Fisher, Marshall L.; Nemhauser, George L.
Management Science, Vol. 23, Issue 8
DOI: 10.1287/mnsc.23.8.789

Approximation for maximizing monotone non-decreasing set functions with a greedy method
journal, January 2014

Wang, Zengfu; Moran, Bill; Wang, Xuezhi
Journal of Combinatorial Optimization, Vol. 31, Issue 1
DOI: 10.1007/s10878-014-9707-3

Alternative Distributed Algorithms for Network Utility Maximization: Framework and Applications
journal, December 2007

Palomar, Daniel P.; Chiang, Mung
IEEE Transactions on Automatic Control, Vol. 52, Issue 12
DOI: 10.1109/TAC.2007.910665

Maximizing Submodular Set Functions Subject to Multiple Linear Constraints
conference, December 2013

Kulik, Ariel; Shachnai, Hadas; Tamir, Tami
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
DOI: 10.1137/1.9781611973068.60

The maximal covering location problem
journal, December 1974

Church, Richard; ReVelle, Charles
Papers of the Regional Science Association, Vol. 32, Issue 1
DOI: 10.1007/BF01942293

Optimal approximation for the submodular welfare problem in the value oracle model
conference, January 2008

Vondrak, Jan
the 40th annual ACM symposium, Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08
DOI: 10.1145/1374376.1374389

Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
journal, January 2011

Calinescu, Gruia; Chekuri, Chandra; Pál, Martin
SIAM Journal on Computing, Vol. 40, Issue 6
DOI: 10.1137/080733991

Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms
journal, April 1977

Cornuejols, Gerard; Fisher, Marshall L.; Nemhauser, George L.
Management Science, Vol. 23, Issue 8
DOI: 10.1287/mnsc.23.8.789

An inequality for polymatroid functions and its applications
journal, September 2003

Boros, E.; Elbassioni, K.; Gurvich, V.
Discrete Applied Mathematics, Vol. 131, Issue 2
DOI: 10.1016/S0166-218X(02)00455-9

Maximizing Submodular Set Functions Subject to Multiple Linear Constraints
conference, December 2013

Kulik, Ariel; Shachnai, Hadas; Tamir, Tami
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
DOI: 10.1137/1.9781611973068.60

Performance bounds for the k-batch greedy strategy in optimization problems with curvature
conference, July 2016

Liu, Yajing; Zhang, Zhenliang; Chong, Edwin K. P.
2016 American Control Conference (ACC)
DOI: 10.1109/ACC.2016.7526805

Tight approximation algorithms for maximum general assignment problems
conference, January 2006

Fleischer, Lisa; Goemans, Michel X.; Mirrokni, Vahab S.
Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06
DOI: 10.1145/1109557.1109624

Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
journal, November 1995

Goemans, Michel X.; Williamson, David P.
Journal of the ACM, Vol. 42, Issue 6
DOI: 10.1145/227683.227684

Approximate Dynamic Programming: Solving the Curses of Dimensionality
book, January 2007

Powell, Warren B.
DOI: 10.1002/9780470182963

Performance bounds for Nash equilibria in submodular utility systems with user groups
journal, October 2017

Liu, Yajing; Chong, Edwin K. P.; Pezeshki, Ali
Journal of Control and Decision, Vol. 5, Issue 1
DOI: 10.1080/23307706.2017.1393355

Optimal approximation for the submodular welfare problem in the value oracle model
conference, January 2008

Vondrak, Jan
the 40th annual ACM symposium, Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08
DOI: 10.1145/1374376.1374389

Transversals and matroid partition
journal, July 1965

Edmonds, J.; Fulkerso, D. R.
Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics, Vol. 69B, Issue 3
DOI: 10.6028/jres.069b.016

A Survey of Multi-Objective Sequential Decision-Making
journal, October 2013

Roijers, D. M.; Vamplew, P.; Whiteson, S.
Journal of Artificial Intelligence Research, Vol. 48
DOI: 10.1613/jair.3987

Streaming submodular maximization: massive data summarization on the fly
conference, January 2014

Badanidiyuru, Ashwinkumar; Mirzasoleiman, Baharan; Karbasi, Amin
Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '14
DOI: 10.1145/2623330.2623637

An analysis of approximations for maximizing submodular set functions—I
journal, December 1978

Nemhauser, G. L.; Wolsey, L. A.; Fisher, M. L.
Mathematical Programming, Vol. 14, Issue 1
DOI: 10.1007/BF01588971

Solving the Generalized Assignment Problem: An Optimizing and Heuristic Approach
journal, August 2003

Nauss, Robert M.
INFORMS Journal on Computing, Vol. 15, Issue 3
DOI: 10.1287/ijoc.15.3.249.16075

RBM4 down-regulates PTB and antagonizes its activity in muscle cell–specific alternative splicing
journal, April 2011

Lin, Jung-Chun; Tarn, Woan-Yuh
Journal of Cell Biology, Vol. 193, Issue 3
DOI: 10.1083/jcb.201007131

Online submodular welfare maximization: Greedy is optimal
conference, December 2013

Kapralov, Michael; Post, Ian; Vondrák, Jan
Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms
DOI: 10.1137/1.9781611973105.88

Tight approximation algorithms for maximum general assignment problems
conference, January 2006

Fleischer, Lisa; Goemans, Michel X.; Mirrokni, Vahab S.
Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06
DOI: 10.1145/1109557.1109624

Extending Polymatroid Set Functions With Curvature and Bounding the Greedy Strategy
conference, June 2018

Liu, Yajing; Chong, Edwin K. P.; Pezeshki, Ali
2018 IEEE Statistical Signal Processing Workshop (SSP)
DOI: 10.1109/SSP.2018.8450732

A submodularity-based approach for multi-agent optimal coverage problems
conference, December 2017

Sun, Xinmiao; Cassandras, Christos G.; Meng, Xiangyu
2017 IEEE 56th Annual Conference on Decision and Control (CDC)
DOI: 10.1109/cdc.2017.8264258

A survey of sensor selection schemes in wireless sensor networks
conference, May 2007

Rowaihy, Hosam; Eswaran, Sharanya; Johnson, Matthew
Defense and Security Symposium, SPIE Proceedings
DOI: 10.1117/12.723514

Submodular Maximization with Cardinality Constraints
conference, January 2014

Buchbinder, Niv; Feldman, Moran; Naor, Joseph (Seffi)
Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms
DOI: 10.1137/1.9781611973402.106

A Unified Continuous Greedy Algorithm for Submodular Maximization
conference, October 2011

Feldman, Moran; Naor, Joseph; Schwartz, Roy
2011 IEEE 52nd Annual Symposium on Foundations of Computer Science (FOCS 2011)
DOI: 10.1109/FOCS.2011.46

An efficient approximation for the Generalized Assignment Problem
journal, November 2006

Cohen, Reuven; Katzir, Liran; Raz, Danny
Information Processing Letters, Vol. 100, Issue 4
DOI: 10.1016/j.ipl.2006.06.003

Distributed Greedy Algorithm for Satellite Assignment Problem with Submodular Utility Function∗∗The work is supported by Lincoln Laboratory with award #7000292526.
journal, January 2015

Qu, Guannan; Brown, Dave; Li, Na
IFAC-PapersOnLine, Vol. 48, Issue 22
DOI: 10.1016/j.ifacol.2015.10.340

A note on maximizing a submodular set function subject to a knapsack constraint
journal, January 2004

Sviridenko, Maxim
Operations Research Letters, Vol. 32, Issue 1
DOI: 10.1016/s0167-6377(03)00062-2

Submodular set functions, matroids and the greedy algorithm: Tight worst-case bounds and some generalizations of the Rado-Edmonds theorem
journal, March 1984

Conforti, Michele; Cornuéjols, Gérard
Discrete Applied Mathematics, Vol. 7, Issue 3
DOI: 10.1016/0166-218X(84)90003-9

Greedy Adaptive Linear Compression in Signal-Plus-Noise Models
journal, April 2014

Liu, Entao; Chong, Edwin K. P.; Scharf, Louis L.
IEEE Transactions on Information Theory, Vol. 60, Issue 4
DOI: 10.1109/TIT.2014.2308258

Dynamic optimization using adaptive control vector parameterization
journal, July 2005

Schlegel, Martin; Stockmann, Klaus; Binder, Thomas
Computers & Chemical Engineering, Vol. 29, Issue 8
DOI: 10.1016/j.compchemeng.2005.02.036

Approximate stochastic dynamic programming for sensor scheduling to track multiple targets
journal, December 2009

Li, Y.; Krakow, L. W.; Chong, E. K. P.
Digital Signal Processing, Vol. 19, Issue 6
DOI: 10.1016/j.dsp.2007.05.004

Towards Robust Multi-Layer Traffic Engineering: Optimization of Congestion Control and Routing
journal, June 2007

He, Jiayue; Bresler, Ma'ayan; Chiang, Mung
IEEE Journal on Selected Areas in Communications, Vol. 25, Issue 5
DOI: 10.1109/JSAC.2007.070602

An approximation algorithm for the generalized assignment problem
journal, February 1993

Shmoys, David B.; Tardos, Éva
Mathematical Programming, Vol. 62, Issue 1-3
DOI: 10.1007/BF01585178

Online Submodular Welfare Maximization: Greedy Beats 1/2 in Random Order
conference, January 2015

Korula, Nitish; Mirrokni, Vahab; Zadimoghaddam, Morteza
Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing - STOC '15
DOI: 10.1145/2746539.2746626

Understanding Cryptography
book, January 2010

Paar, Christof; Pelzl, Jan
DOI: 10.1007/978-3-642-04101-3

Improved bounds for the greedy strategy in optimization problems with curvature
journal, August 2018

Liu, Yajing; Chong, Edwin K. P.; Pezeshki, Ali
Journal of Combinatorial Optimization, Vol. 37, Issue 4
DOI: 10.1007/s10878-018-0345-z

Non-Cooperative Games
journal, September 1951

Nash, John
The Annals of Mathematics, Vol. 54, Issue 2
DOI: 10.2307/1969529

Online Submodular Welfare Maximization: Greedy Beats 1/2 in Random Order
preprint, January 2017

Korula, Nitish; Mirrokni, Vahab; Zadimoghaddam, Morteza
arXiv
DOI: 10.48550/arxiv.1712.05450

The budgeted maximum coverage problem
journal, April 1999

Khuller, Samir; Moss, Anna; Naor, Joseph (Seffi)
Information Processing Letters, Vol. 70, Issue 1
DOI: 10.1016/S0020-0190(99)00031-9

P-Complete Approximation Problems
journal, July 1976

Sahni, Sartaj; Gonzalez, Teofilo
Journal of the ACM (JACM), Vol. 23, Issue 3
DOI: 10.1145/321958.321975

Editorial
journal, July 2009

harris, fred; Rangaswamy, Murali
Digital Signal Processing, Vol. 19, Issue 4
DOI: 10.1016/j.dsp.2009.04.004

Bounding the greedy strategy in finite-horizon string optimization
conference, December 2015

Liu, Yajing; Chong, Edwin K. P.; Pezeshki, Ali
2015 54th IEEE Conference on Decision and Control (CDC)
DOI: 10.1109/CDC.2015.7402826

Utility-based rate control in the Internet for elastic traffic
journal, April 2002

La, R. J.; Anantharam, V.
IEEE/ACM Transactions on Networking, Vol. 10, Issue 2
DOI: 10.1109/90.993307

A Survey of Multi-Objective Sequential Decision-Making
journal, October 2013

Roijers, D. M.; Vamplew, P.; Whiteson, S.
Journal of Artificial Intelligence Research, Vol. 48
DOI: 10.1613/jair.3987

Online submodular welfare maximization: Greedy is optimal
conference, December 2013

Kapralov, Michael; Post, Ian; Vondrák, Jan
Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms
DOI: 10.1137/1.9781611973105.88

Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions
conference, January 2002

Vetta, A.
The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
DOI: 10.1109/SFCS.2002.1181966

Maximising Real-Valued Submodular Functions: Primal and Dual Heuristics for Location Problems
journal, August 1982

Wolsey, Laurence A.
Mathematics of Operations Research, Vol. 7, Issue 3
DOI: 10.1287/moor.7.3.410

Performance Bounds with Curvature for Batched Greedy Optimization
journal, March 2018

Liu, Yajing; Zhang, Zhenliang; Chong, Edwin K. P.
Journal of Optimization Theory and Applications, Vol. 177, Issue 2
DOI: 10.1007/s10957-017-1177-1

Maximizing a class of submodular utility functions
journal, August 2009

Ahmed, Shabbir; Atamtürk, Alper
Mathematical Programming, Vol. 128, Issue 1-2
DOI: 10.1007/s10107-009-0298-1

Autonomous Vehicle-Target Assignment: A Game-Theoretical Formulation
journal, April 2007

Arslan, Gürdal; Marden, Jason R.; Shamma, Jeff S.
Journal of Dynamic Systems, Measurement, and Control, Vol. 129, Issue 5
DOI: 10.1115/1.2766722

Improved Bounds for Matroid Partition and Intersection Algorithms
journal, November 1986

Cunningham, William H.
SIAM Journal on Computing, Vol. 15, Issue 4
DOI: 10.1137/0215066

String Submodular Functions With Curvature Constraints
journal, March 2016

Zhang, Zhenliang; Chong, Edwin K. P.; Pezeshki, Ali
IEEE Transactions on Automatic Control, Vol. 61, Issue 3
DOI: 10.1109/TAC.2015.2440566

A submodular optimization framework for leader selection in linear multi-agent systems
conference, December 2011

Clark, Andrew; Poovendran, Radha
2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011)
DOI: 10.1109/CDC.2011.6160248

Selecting Sequences of Items via Submodular Maximization
journal, February 2017

Tschiatschek, Sebastian; Singla, Adish; Krause, Andreas
Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 31, Issue 1
DOI: 10.1609/aaai.v31i1.10923

Similar Records in DOE PAGES and OSTI.GOV collections:

A General Framework for Bounding Approximate Dynamic Programming Schemes

Journal Article Liu, Yajing ; Chong, Edwin K. P. ; Pezeshki, Ali ; ... - IEEE Control Systems Letters

For years, there has been interest in approximation methods for solving dynamic programming problems, because of the inherent complexity in computing optimal solutions characterized by Bellman’s principle of optimality. A wide range of approximate dynamic programming (ADP) methods now exists. It is of great interest to guarantee that the performance of an ADP scheme be at least some known fraction, say ß , of optimal. This letter introduces a general approach to bounding the performance of ADP methods, in this sense, in the stochastic setting. The approach is based on new results for bounding greedy solutions in string optimization problems,more »« less
https://doi.org/10.1109/LCSYS.2020.3003477
PREEMPT: Scalable Epidemic Interventions Using Submodular Optimization on Multi-GPU Systems

Conference Minutoli, Marco ; Sambaturu, Prathyush ; Halappanavar, Mahantesh ; ...

Preventing and slowing the spread of epidemics is achieved through techniques such as vaccination and social distancing. Given practical limitations on the number of vaccines and cost of administration, optimization becomes a necessity. Previous approaches using mathematical programming methods have shown to be effective but are limited by computational costs. In this work, we make several contributions: First, we present a new approach for intervention via maximizing the influence of vaccinated nodes on the network. We call this method \preempt. Next, we prove submodular properties associated with the objective function of our method so that it aids in construction of an efficient greedy approximation strategy. Consequently, we present a new parallel algorithm based on greedy hill climbing for \preempt, and present an efficient parallel implementation for distributed CPU-GPU heterogeneous platforms. Our results demonstrate that \preempt{} is able to achieve a significant reduction (up to 6.75more »« less
Optimal interdiction of unreactive Markovian evaders

Conference Gutfraind, Alexander ; Hagberg, Aric ; Pan, Feng

The network interdiction problem arises in a wide variety of areas including military logistics, infectious disease control and counter-terrorism. In the classical formulation one is given a weighted network G(N, E) and the task is to find b nodes (or edges) whose removal would maximally increase the least-cost path from a source node s to a target node r. In practical applications. G represenLs a transportation or activity network; node/edge removal is done by an agent, the 'interdictor' against another agent the 'evader' who wants to traverse G from s to t along the least-cost route. Our work is motivatedmore »« less
https://doi.org/10.1007/978-3-642-01929-6_9

Full Text Available
Optimal interdiction of unreactive Markovian evaders

Conference Hagberg, Aric ; Pan, Feng ; Gutfraind, Alex

The interdiction problem arises in a variety of areas including military logistics, infectious disease control, and counter-terrorism. In the typical formulation of network interdiction. the task of the interdictor is to find a set of edges in a weighted network such that the removal of those edges would increase the cost to an evader of traveling on a path through the network. Our work is motivated by cases in which the evader has incomplete information about the network or lacks planning time or computational power, e.g. when authorities set up roadblocks to catch bank robbers, the criminals do not knowmore »« less
Full Text Available
Is submodularity testable?

Conference Vondrak, Jan ; Seshadhri, Comandur

We initiate the study of property testing of submodularity on the boolean hypercube. Submodular functions come up in a variety of applications in combinatorial optimization. For a vast range of algorithms, the existence of an oracle to a submodular function is assumed. But how does one check if this oracle indeed represents a submodular function? Consider a function f: {l_brace}0, 1{r_brace}{sup n} {yields} R. The distance to submodularity is the minimum fraction of values of f that need to be modified to make f submodular. If this distance is more than {epsilon} > 0, then we say that f ismore »« less

Similar Records

Title: Submodular optimization problems and greedy strategies: A survey

Abstract

Citation Formats

Optimization Strategies in Adaptive Control: A Selective Survey journal, January 1975

Maximizing a Monotone Submodular Function Subject to a Matroid Constraint journal, January 2011

Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms journal, April 1977

Approximation for maximizing monotone non-decreasing set functions with a greedy method journal, January 2014

Alternative Distributed Algorithms for Network Utility Maximization: Framework and Applications journal, December 2007

Maximizing Submodular Set Functions Subject to Multiple Linear Constraints conference, December 2013

The maximal covering location problem journal, December 1974

Optimal approximation for the submodular welfare problem in the value oracle model conference, January 2008

Maximizing a Monotone Submodular Function Subject to a Matroid Constraint journal, January 2011

Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms journal, April 1977

An inequality for polymatroid functions and its applications journal, September 2003

Maximizing Submodular Set Functions Subject to Multiple Linear Constraints conference, December 2013

Performance bounds for the k-batch greedy strategy in optimization problems with curvature conference, July 2016

Tight approximation algorithms for maximum general assignment problems conference, January 2006

Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming journal, November 1995

Approximate Dynamic Programming: Solving the Curses of Dimensionality book, January 2007

Performance bounds for Nash equilibria in submodular utility systems with user groups journal, October 2017

Optimal approximation for the submodular welfare problem in the value oracle model conference, January 2008

Transversals and matroid partition journal, July 1965

A Survey of Multi-Objective Sequential Decision-Making journal, October 2013

Streaming submodular maximization: massive data summarization on the fly conference, January 2014

An analysis of approximations for maximizing submodular set functions—I journal, December 1978

Solving the Generalized Assignment Problem: An Optimizing and Heuristic Approach journal, August 2003

RBM4 down-regulates PTB and antagonizes its activity in muscle cell–specific alternative splicing journal, April 2011

Online submodular welfare maximization: Greedy is optimal conference, December 2013

Tight approximation algorithms for maximum general assignment problems conference, January 2006

Extending Polymatroid Set Functions With Curvature and Bounding the Greedy Strategy conference, June 2018

A submodularity-based approach for multi-agent optimal coverage problems conference, December 2017

A survey of sensor selection schemes in wireless sensor networks conference, May 2007

Submodular Maximization with Cardinality Constraints conference, January 2014

A Unified Continuous Greedy Algorithm for Submodular Maximization conference, October 2011

An efficient approximation for the Generalized Assignment Problem journal, November 2006

Distributed Greedy Algorithm for Satellite Assignment Problem with Submodular Utility Function∗∗The work is supported by Lincoln Laboratory with award #7000292526. journal, January 2015

A note on maximizing a submodular set function subject to a knapsack constraint journal, January 2004

Submodular set functions, matroids and the greedy algorithm: Tight worst-case bounds and some generalizations of the Rado-Edmonds theorem journal, March 1984

Greedy Adaptive Linear Compression in Signal-Plus-Noise Models journal, April 2014

Dynamic optimization using adaptive control vector parameterization journal, July 2005

Approximate stochastic dynamic programming for sensor scheduling to track multiple targets journal, December 2009

Towards Robust Multi-Layer Traffic Engineering: Optimization of Congestion Control and Routing journal, June 2007

An approximation algorithm for the generalized assignment problem journal, February 1993

Online Submodular Welfare Maximization: Greedy Beats 1/2 in Random Order conference, January 2015

Understanding Cryptography book, January 2010

Improved bounds for the greedy strategy in optimization problems with curvature journal, August 2018

Non-Cooperative Games journal, September 1951

Online Submodular Welfare Maximization: Greedy Beats 1/2 in Random Order preprint, January 2017

The budgeted maximum coverage problem journal, April 1999

P-Complete Approximation Problems journal, July 1976

Editorial journal, July 2009

Bounding the greedy strategy in finite-horizon string optimization conference, December 2015

Utility-based rate control in the Internet for elastic traffic journal, April 2002

A Survey of Multi-Objective Sequential Decision-Making journal, October 2013

Online submodular welfare maximization: Greedy is optimal conference, December 2013

Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions conference, January 2002

Maximising Real-Valued Submodular Functions: Primal and Dual Heuristics for Location Problems journal, August 1982

Performance Bounds with Curvature for Batched Greedy Optimization journal, March 2018

Maximizing a class of submodular utility functions journal, August 2009

Autonomous Vehicle-Target Assignment: A Game-Theoretical Formulation journal, April 2007

Improved Bounds for Matroid Partition and Intersection Algorithms journal, November 1986

String Submodular Functions With Curvature Constraints journal, March 2016

A submodular optimization framework for leader selection in linear multi-agent systems conference, December 2011

Selecting Sequences of Items via Submodular Maximization journal, February 2017

Optimization Strategies in Adaptive Control: A Selective Survey
journal, January 1975

Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
journal, January 2011

Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms
journal, April 1977

Approximation for maximizing monotone non-decreasing set functions with a greedy method
journal, January 2014

Alternative Distributed Algorithms for Network Utility Maximization: Framework and Applications
journal, December 2007

Maximizing Submodular Set Functions Subject to Multiple Linear Constraints
conference, December 2013

The maximal covering location problem
journal, December 1974

Optimal approximation for the submodular welfare problem in the value oracle model
conference, January 2008

Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
journal, January 2011

Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms
journal, April 1977

An inequality for polymatroid functions and its applications
journal, September 2003

Maximizing Submodular Set Functions Subject to Multiple Linear Constraints
conference, December 2013

Performance bounds for the k-batch greedy strategy in optimization problems with curvature
conference, July 2016

Tight approximation algorithms for maximum general assignment problems
conference, January 2006

Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
journal, November 1995

Approximate Dynamic Programming: Solving the Curses of Dimensionality
book, January 2007

Performance bounds for Nash equilibria in submodular utility systems with user groups
journal, October 2017

Optimal approximation for the submodular welfare problem in the value oracle model
conference, January 2008

Transversals and matroid partition
journal, July 1965

A Survey of Multi-Objective Sequential Decision-Making
journal, October 2013

Streaming submodular maximization: massive data summarization on the fly
conference, January 2014

An analysis of approximations for maximizing submodular set functions—I
journal, December 1978

Solving the Generalized Assignment Problem: An Optimizing and Heuristic Approach
journal, August 2003

RBM4 down-regulates PTB and antagonizes its activity in muscle cell–specific alternative splicing
journal, April 2011

Online submodular welfare maximization: Greedy is optimal
conference, December 2013

Tight approximation algorithms for maximum general assignment problems
conference, January 2006

Extending Polymatroid Set Functions With Curvature and Bounding the Greedy Strategy
conference, June 2018

A submodularity-based approach for multi-agent optimal coverage problems
conference, December 2017

A survey of sensor selection schemes in wireless sensor networks
conference, May 2007

Submodular Maximization with Cardinality Constraints
conference, January 2014

A Unified Continuous Greedy Algorithm for Submodular Maximization
conference, October 2011

An efficient approximation for the Generalized Assignment Problem
journal, November 2006

Distributed Greedy Algorithm for Satellite Assignment Problem with Submodular Utility Function∗∗The work is supported by Lincoln Laboratory with award #7000292526.
journal, January 2015

A note on maximizing a submodular set function subject to a knapsack constraint
journal, January 2004

Submodular set functions, matroids and the greedy algorithm: Tight worst-case bounds and some generalizations of the Rado-Edmonds theorem
journal, March 1984

Greedy Adaptive Linear Compression in Signal-Plus-Noise Models
journal, April 2014

Dynamic optimization using adaptive control vector parameterization
journal, July 2005

Approximate stochastic dynamic programming for sensor scheduling to track multiple targets
journal, December 2009

Towards Robust Multi-Layer Traffic Engineering: Optimization of Congestion Control and Routing
journal, June 2007

An approximation algorithm for the generalized assignment problem
journal, February 1993

Online Submodular Welfare Maximization: Greedy Beats 1/2 in Random Order
conference, January 2015

Understanding Cryptography
book, January 2010

Improved bounds for the greedy strategy in optimization problems with curvature
journal, August 2018

Non-Cooperative Games
journal, September 1951

Online Submodular Welfare Maximization: Greedy Beats 1/2 in Random Order
preprint, January 2017

The budgeted maximum coverage problem
journal, April 1999

P-Complete Approximation Problems
journal, July 1976

Editorial
journal, July 2009

Bounding the greedy strategy in finite-horizon string optimization
conference, December 2015

Utility-based rate control in the Internet for elastic traffic
journal, April 2002

A Survey of Multi-Objective Sequential Decision-Making
journal, October 2013

Online submodular welfare maximization: Greedy is optimal
conference, December 2013

Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions
conference, January 2002

Maximising Real-Valued Submodular Functions: Primal and Dual Heuristics for Location Problems
journal, August 1982

Performance Bounds with Curvature for Batched Greedy Optimization
journal, March 2018

Maximizing a class of submodular utility functions
journal, August 2009

Autonomous Vehicle-Target Assignment: A Game-Theoretical Formulation
journal, April 2007

Improved Bounds for Matroid Partition and Intersection Algorithms
journal, November 1986

String Submodular Functions With Curvature Constraints
journal, March 2016

A submodular optimization framework for leader selection in linear multi-agent systems
conference, December 2011

Selecting Sequences of Items via Submodular Maximization
journal, February 2017