Current
and recent courses: Math
4630/5630 Discrete Modeling and Optimization
Math 3050 Discrete
Mathematics
Math 3200/5200 Applied
Linear Algebra
Math 306 Foundations of
Mathematics I
Math 442/542 Theory
Linear and Nonlinear Programming
Math 263a Calculus I
Math 263b Calculus II
Math 250 Probability and
Statistics I
Combinatorial Optimization
Mathematical Programming
Approximation Algorithms
Network Design Problems
Applications of Operations Research
The primary focus of my research is on the design and analysis of algorithms for fundamental problems in network, combinatorial optimization, approximation algorithms, linear and integer programming, and their applications to various problems. Most combinatorial optimization problems are NP-hard. I am interested in developing approximation algorithms for them, that is, algorithms which are fast and provide provably close-to-optimal solutions for the problems. My goal is to design algorithms which have both decent theoretical guarantees and good practical performance.
Selected Publications
V. Melkonian
”Circuit
integration through lattice hyperterms "
Discrete Mathematics, Algorithms and Applications, Vol.
3(1), 101-119, 2011.
V. Lskavyan and V. Melkonian
“A computational model of politicians–bureaucracy relationship in a
competitively authoritarian environment”
Int. J. Computational Economics and
Econometrics, Vol. 2(1), 1-23, 2011.
V. Melkonian
”LP-based solution
methods for asymmetric TSP "
Information Processing Letters, Vol. 101(6),
233-238, 2007.
V. Melkonian
"New
Primal-Dual Algorithms for Steiner Tree Problems"
Computers and Operations Research, Vol. 34(7),
2147-2167, 2007.
V. Melkonian
" Flows in
dynamic networks with aggregate arc capacities "
Information Processing Letters, Vol. 101(1), 30-35,
2007.
V. Melkonian and E . Tardos .
"Primal-Dual-Based
Algorithms for a Directed Network Design Problem"
INFORMS Journal on Computing, Vol. 17(2),
159-174, 2005.
R. Roundy, D. Chen, P. Chen, M. Cakanyildirim,
M.B. Freimer, V. Melkonian.
"Capacity-Driven
Acceptance of Customer Orders for a Multi-Stage Batch Manufacturing
System: Models and Algorithms"
IIE Transactions on
Scheduling and Logisitics, Vol. 37(12),
1093-1105, 2005.
V. Melkonian and E . Tardos .
"Algorithms
for a Network Design Problem with Crossing Supermodular
Demands"
Networks,
Vol. 43(4), 256-265, 2004.
Some links to Operations Research / Computer Science resources