- Department
of Mathematics

Ohio University

Athens, OH 45701 - E-mail: melkonia@ohio.edu
- Office: Morton Hall 543
- Phone: (740)593-1276

**Current
and recent courses**: Math
4620/5620 Linear and Nonlinear Optimization

Math 3050 Discrete
Mathematics

Math 4630/5630 Discrete
Modeling and Optimization

Math 3200/5200 Applied
Linear Algebra

Math 306 Foundations of
Mathematics I

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 " __

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