photoColonel Steven B. Horton

Colonel Steven B. Horton is Professor of Operations Research at the United States Military Academy.  He is a Professor, United States Military Academy (PUSMA) and the Deputy Department Head for the Department of Mathematical Sciences.  His office is 238A Thayer Hall and his phone is (845) 938-5870.  You can email him by clicking here.  In the fall of 2008, he is teaching Mathematical Modeling and Introduction to Calculus (MA103).



Publications

G. McCormick, S. Horton, and L. Harrison.  Things fall apart: the "end game" dynamics of internal wars.  Accepted for publication in Third World Quarterly, 28 (2007).

M. Huber and S. Horton.  How Ken Griffey, Jr. is like Kevin Bacon or, degrees of separation in baseball.  Journal of Recreational Mathematics, 33 (2006), pp. 194-203.

R. Gera, C. Rasmussen, P. Stanica, and S. Horton.  Results on the Min-Sum Vertex Cover Problem.  Congressus Numerantium 178 (2006), pp 161-172.

R. Gera, C. Rasmussen, and S. Horton.  Dominator Colorings and Safe Clique Partitions.  Congressus Numerantium 181 (2006), pp. 19-32.

Steven B. Horton.  On Some Problems Related to Dominating Set.  Graph Theory Notes of New York 48 (2005).

Jean R.S. Blair, Wayne Goddard, Stephen T. Hedetniemi, Steven B. Horton, Patrick Jones, and Grzegorz Kubicki .  On Domination and Reinforcement Numbers in Trees.  Accepted for publication in Discrete Math (2007).

J. R. S. Blair and S. B. Horton.  Broadcast Covers in Graphs.  Congressus Numerantium 173 (2005), pp 109-115.

J. R. S. Blair, S. B. Horton, S. T. Hedetniemi, S. M. Hedetniemi, W. Goddard.  Domination Equivalence: Algorithms and Complexity.  AKCE International Journal of Graphs and Combinatorics 2 (2005), pp 123-136.

J. R. S. Blair, P. Heggernes, S. B. Horton, and F. Manne.  Broadcast Domination Algorithms for Interval Graphs, Series-Parallel Graphs, and Trees.  Congressus Numerantium 169 (2004), pp 55-77.

S. B. Horton, T. Easton, and R. G. Parker.  The Linear Arrangement Problem on Recursively Constructed Graphs.  Networks 42(3) (2003), pp. 165-168.

T. Easton, S.B. Horton, R.G. Parker.  On the Complexity of Certain Completion Problems.  Congressus Numerantium 145 (2000), pp 9-31.

S.B. Horton, W. Jerzak, A.A. Napoli, and N. Prins.  A Math, Science, and Technology Interdisciplinary Lively Application of Mathematics at the United States Military Academy.  Primus Vol. 10, Number 1 (2000), pp 42-52.

S.B. Horton, R.G. Parker, R.B. Borie.  On Minimum Cuts and the Linear Arrangement Problem.  Discrete Applied Mathematics 103 (2000), pp 127-139.

T. Easton, S.B. Horton, R.G. Parker.  A Solvable Case of the Optimal Linear Arrangement Problem on Halin Graphs. Congressus Numerantium 119 (1996), pp 3-17.

S.B. Horton, R.G. Parker.  On Halin Subgraphs and Supergraphs. Discrete Applied Mathematics 56 (1995), pp 19-35.

W.P. Fox, S.B. Horton.  A "7 into 4" Carry Through Problem. Primus Vol. 5, Number 2 (1995), pp 163-177.

R.B. Borie, S.B. Horton, R.G. Parker.  On Some Results Pertaining to Halin Graphs. Congressus Numerantium 89 (1992), pp 65-87.

S.B. Horton.  The Optimal Linear Arrangement Problem:  Algorithms and Approximation.  Ph.D. Thesis, Georgia Institute of Technology (1997).

S.B. Horton.  Graph Approximation:  Issues and Complexity.  M.S. Thesis, Georgia Institute of Technology (1991).


Invited Presentations

S. B. Horton and R.X. Sturdivant.  Discrete Dynamical Systems and Problem Solving.  Minicourse given at the Joint Mathematics Meeting, San Antonio, TX (January 2006).

S. B. Horton.  Some Problems Related to Dominating Set.  Invited talk given to the graduate seminar in the Department of Industrial Engineering and Operations Research, University of California at Berkeley (October 2005).

S. B. Horton.  A Graph Theory Primer.  This was a three day graph theory seminar conducted for officials  at the Army Research Office in Research Triangle Park, North Carolina (August 2005), by invitation of the director of the mathematical sciences division.

S. B. Horton.  Some Problems Related to Domination in Graphs.  Graph Theory Day Forty Eight, sponsored by the New York Academy of Sciences, Mount Saint Mary College, Newburgh, NY (13 November 2004).

G. Krahn, M. Huber, S. Horton, M. Phillips, J Myers, A Glen.  The Continuous Evolution of Core Mathematics.  New York Project Kaleidescope Assembly for Shaping General Education Programs Focused on Scientific and Quantitative Literacy, New York, NY (2003).

A. Durfee, S.B. Horton, R. Peck, A. Rossman.  Integrating Statistics/Data Analysis through the Core Curriculum.  Panel Discussion at the Joint Mathematics Meetings, San Diego, California (2002).

R.B. Borie, S.B. Horton*, R.G. Parker.  On Cuts of Bounded Order and the Linear Arrangement Problem.  INFORMS, Philadelphia, Pennsylvania (1999).

Contributed Presentations

M. Huber*, S. B. Horton*, T. Povich, and D. Hunt.  Teaching Differential Equations With Modeling and Without Integration.  Joint Mathematics Meetings, Atlanta, GA (2005). 

J. R. S. Blair, P. Heggernes, S. B. Horton*, and F. Manne.  Broadcast Domination Algorithms for Interval Graphs, Series-Parallel Graphs, and Trees.  35th International Conference on Combinatorics, Graph Theory, and Computing, Florida Atlantic University, Boca Raton, Florida (2004).

J. A. Picciuto, S. B. Horton.  Projects in a Probability and Statistics Course at West Point.  Joint Mathematics Meetings, Baltimore, MD (2003). 

D. Hughes Hallett, S.B. Horton, A. Rossman, K. Somers, R. Starbuck.  The Role of Undergraduate Mathematics for Statistics and vice-versa.  Panel Discussion at the Joint Statistics Meeting, New York City (2002).

D.C. Arney, S.B. Horton*.  On the Value of Information.  69th Military Operations Research Society Symposium, United States Naval Academy, Annapolis, Maryland (2001).

P.F. Beaver*, S.B. Horton.  A Linear Model to support USSOCOM's Strategic Planning Process.  68th Military Operations Research Society Symposium, United States Air Force Academy, Colorado Springs, Colorado (2000).

S.B. Horton*, T. Easton, and R.G. Parker.  On the Complexity of Certain Completion Problems.  31st International Conference on Combinatorics, Graph Theory, and Computing, Florida Atlantic University, Boca Raton, Florida (2000).

G.W. Krahn*, S.B. Horton*.  Knowledge and Reasoning – What is the Relation?  Joint Mathematics Meetings, Washington, D.C. (2000).

S.B. Horton*, D.J. Day.  Teaching Statistical Reasoning at West Point.  Joint Mathematics Meetings, Washington, D.C. (2000).

D.C. Arney*, J. Myers*, R. Marchand*, S.B. Horton*, E.J. Berkove*, M. Vanesko*, J. Scharf*.  A Guided Tour of Project INTERMATH Application Projects.  Joint Mathematics Meetings, Washington, D.C. (2000).

S.B. Horton*, A.A. Napoli*, and D.J. Day*.  Math, Science, and Technology Interdisciplinary Lively Applications of Mathematics (MST ILAPs).  Educating Army Leaders, West Point, NY (1999).

S.B. Horton*, A.A. Napoli, W. Jerzak, and E.J. Berkove.  A Math, Science, and Technology Interdisciplinary Lively Application of Mathematics at the United States Military Academy.  Joint Mathematics Meetings, San Antonio, Texas (1999).

S.B. Horton*, W.P. Fox, G.W. Krahn, and W.G. Wilhelm.  Digitization for the Army After Next.  66th Military Operations Research Society Symposium, Naval Postgraduate School, Monterey, California (1998).

G.W. Krahn*, K.G. Snook*, D.C. Daughtry, S.B. Horton*, and W.P. Fox*.  Math, Methods, and Models.  Teaching That Leads to Learning:  A Celebration of Teaching Strategies That Work, West Point, NY (1997).

S.B. Horton*, T. Easton, and R.G. Parker.  A Solvable Case of the Optimal Linear Arrangement Problem on Halin Graphs.  27th International Conference on Combinatorics, Graph Theory, and Computing, Louisiana State University, Baton Rouge, Louisiana (1996).

S.B. Horton* and R.G. Parker.  On Some Results Pertaining to Halin Graphs.   23rd International Conference on Combinatorics, Graph Theory, and Computing, Florida Atlantic University, Boca Raton, Florida (1992).

* Denotes presenting author(s).


Other Publications

Steven B. Horton, Claudio N. De Meneses, M. Erol Uluçakli, Arup Mukherjee.  A Computational Study of the Broadcast Domination Problem.  DIMACS Technical Report number 2004-45 (2004).

S.B. Horton, D. Day, A. Napoli, B. Barraclough, G. Hansler, J. Samek.  Analyzing the Safety of a Dam.  In Changing Core Mathematics, edited by C. Arney and D. Small.  Mathematical Association of America (2002), pp 179-181.

S.B. Horton.  An Interdisciplinary Project at USMA.  Mathematica Militaris, Vol 9, Issue 1, (Spring 1999).

S.B. Horton.  The United States Military Academy at West Point.  Phalanx, Vol 32, No. 1 (March 1999).

S.B. Horton, K. Michaelson.  Working Groups/Composite Groups and the 67th Military Operations Research Society Symposium.  Phalanx, Vol 31, No. 4 (December 1998).

S.B. Horton.  Student Growth Assessment at USMA.  Mathematica Militaris, Vol 8, Issue 3, Fall 1998.

W.P. Fox, S.B. Horton.  Military Applications of Reliability.  Military Mathematical Modeling.  Defense Automated Printing Services, West Point, NY (1998) pp 153-168.

J.A. Appleget, S.B. Horton.  Military Applications of Network Flows.  Military Mathematical Modeling. Defense Automated Printing Services, West Point, NY (1998) pp 141-150.

Co-author (with Joe Malkevitch) of the Communications Network Problem for the 1994 Mathematical Competition in Modeling (MCM).  This problem was published, along with some student solutions and other comments, in the UMAP Journal, special edition, MCM: The First Ten Years, published by COMAP (1995).
 


Selected Co-Authors

R. Gary Parker (Georgia Tech)

Richard Borie (University of Alabama)

Bill Fox (Francis Marion University)

Todd Easton (Kansas State University)

Jean Blair (EECS, USMA)

Pinar Heggernes (University of Bergen, Norway)

Fredrik Manne (University of Bergen, Norway)

Wayne Goddard (Clemson University)

Steve Hedetniemi (Clemson University)

Sandee Hedetniemi (Clemson University)

Grzegorz Kubicki (University of Louisville)

Claudio N. de Meneses (University of Florida)

M. Erol Uluçakli (Lafayette College)

Arup Mukherjee (Montclair State University)

Ralucca Gera (Naval Postgraduate School)

Craig Rasmussen (Naval Postgraduate School)

Pante Stanica (Naval Postgraduate School)


Committees and Additional Responsibilities

National and International Level

Member of the COMAP Subcommittee of the INFORMS Education Committee 2001-2003.

Invited participant at the Mathematical Association of America's Committee on the Undergraduate Program in Mathematics (CUPM) Calculus Reform and the First Two Years (CRAFTY) Subcommittee's workshop on Statistics (whew!) conducted at Grinnell College in October, 2000.  Click here to view our report from the meeting.

Deputy Site Coordinator for the 67th Military Operations Research Society Symposium that was conducted at West Point in June, 1999.

Academy Level

Member of the Dean's Committee that awards grants from the Faculty Development and Research Fund for fiscal years 2004 and 2005.

Member of the USMA Curriculum Committee 2001-2003.

Member of the Dean's Math, Science, and Technology Goal Committee 1999-2000.

Member of the Dean's Committee to select Academy Professors for the Department of Electrical Engineering and Computer Science in 2001.

Member of several committees to select rotating military faculty for the Department of Mathematical Sciences.

Member of the Hollis Award Committees for 1998, 1999, 2000, and 2002.  The Hollis Award is given annually to the cadet team that submits the best operations research project at USMA.

 


Memberships

Fellow of the Institute of Combinatorics and its Applications

Mathematical Association of America

Institute for Operations Research and the Management Sciences (INFORMS)

Association of Graduates, USMA

Pi Mu Epsilon


Research Interests

My research interests include combinatorial optimization, graph theory, computational complexity, and approximation algorithms.  My Ph.D. thesis dealt with the optimal linear arrangement problem (OLA).   Given a graph G = (V,E), an optimal linear arrangement is a one-to-one function that maps V onto the integers {1, 2, 3, ..., |V|} in such a way that the sum (over all edges in the graph) of the absolute differences of the vertex labels is minimized.  My thesis gives new algorithms for OLA as well as new algorithms, heuristics, and complexity results for some related problems.  Subsequent research in this field has included new results in computational complexity for certain "partially completed" linear arrangement problems, as well as partially completed Latin squares.  I am also interested in problems related to DOMINATING SET, such as broadcast domination, parity domination, and other variants of domination in graphs.

My other academic interests are stochastic processes, simulation, and probability and statistics. 


Brief Biography

I entered the United States Military Academy in 1978 from Michigan, and graduated in 1982.   Following graduation, I served as an engineer platoon leader in the 92nd Engineer Battalion at Fort Stewart, Georgia, and as the Deputy Director of Engineering and Housing at United States Army Field Station Sinop in Sinop, Turkey.

After attending the Engineer Officer Advanced Course in 1986, I was assigned to the 4th Engineer Battalion at Fort Carson, Colorado where I served as an Assistant Operations Officer, Battalion Adjutant, and Company Commander of Echo Company, 4th Engineers.

I started graduate school in the fall of 1989 at the Georgia Institute of Technology.  I earned a Master of Science in Operations Research in 1991, and reported to the Department of Mathematical Sciences, USMA, in the fall of 1991. I taught MA103 (Discrete Dynamical Systems), MA205 (Multivariable Calculus), and MA206 (Probability and Statistics) and served as the course director for MA372 (Introduction to Discrete Mathematics) and MA476 (Mathematical Statistics).  I also developed and taught an MA489 course in Graph Theory.  In addition, I was a department academic counselor and an officer representative for the Army Men's Basketball Team.

I then returned to graduate school in the fall of 1994 and completed my Ph.D. at Georgia Tech in Industrial and Systems Engineering in June of 1997 under the able guidance of Professor R. Gary Parker.  I reported back to the Department of Mathematical Sciences in the summer of 1997, serving as an assistant professor and the program director for MA206, as well as the course director for MA492D (Graph Theory and Networks), and instructor for MA376 (Applied Statistics).  I was selected for an academy professorship and advanced to the academic rank of associate professor in January 1999.  

I spent the 2000-2001 academic year attending the Industrial College of the Armed Forces at Fort McNair in Washington D.C. where I earned a Master's degree in National Resource Strategy.  Since returning to the Department in the summer of 2001, I have been involved in curriculum design and reform issues for my department and the Academy.  I also served again as the program director for MA206 from August 2001 until December 2002.  From December 2002 to January 2004, I was the Acting Deputy Head of the Department of Mathematical Sciences.  Outside of the classroom, I am an Officer Representative for the Army Men's Basketball Team and the liaison professor for the Georgia Institute of Technology.

I spent the academic year starting in the summer of 2005 on sabbatical in the Department of Defense Analysis at the Naval Postgraduate School in Monterey, California.

My outside interests include many sports (basketball, golf, tennis, softball, etc.), duplicate bridge, and the guitar.


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Last updated: 26 February 2008
Updated by: COL Horton