RESEARCH TOPICS FOR STUDENTS (Dr. Mark Sh. Levin)

(levels: BS, MS, PhD, …)

I.Mathematical and Algorithmic Issues

1.1.Models for proximity and sub/super-structures (PhD, MS):

(i)proximity for structures (graphs, networks)

(ii)substructures and superstructures for graphs/networks

1.2.Hierarchical algorithm systems (PhD, MS):

(i)design of parallel-series problem solving strategies

(ii)exchange techniques for scheduling problems

1.3.Heuristics, macroheuristics, and computer experiments (PhD, MS, BS):

(i)partitioning/synthesis macroheuristic for combinatorial optimization problems

(e.g., scheduling, multiple choice problem, TSP, minimal Steiner-tree problem,

assignment/allocation problem, hotlink problem, graph-coloring)

(ii)heuristics (e.g., cross-entropy method, space-filling curves technique)

1.4.Heuristics based on discrete space/lattices for quality of solutions

for multicriteria combinatorial optimization problems (PhD, MS, BS):

(i)knapsack problem, multiple choice problem,

(ii)the shortest path problem,

(iii)graph approximation problem,

(iv)spanning tree problem,

(v)Steiner tree problem,

(vi)traveling salesman problem (TSP),

(vii)assignment/allocation problems, and

(viii) scheduling problems.

1.5.Partitioning of graphs/networks (e.g., partitioning a call graph) (PhD, MS, BS)

1.6.Restructuring in combinatorial optimization (PhD, MS, BS):

(i)knapsack problem, multiple choice problem,

(ii)the shortest path problem,

(iii)assignment/allocation problems,

(iv)spanning tree problem,

(v)Steiner tree problem,

(vi)traveling salesman problem (TSP),

(vii) hotlink problems, and

(viii) scheduling problems.

II.Hierarchical Morphological Design

2.1.Seven technological problems (MS, BS):

(i)hierarchical modeling of composite (modular) system

(ii)system design

(iii)system evaluation

(iv)revelation of bottlenecks

(v)redesign/improvement/adaptation

(vi)multistage design or design of system trajectory

(vii)combinatorial modeling of system evolution/development

2.2.Modular design of multi-product systems (PhD, MS, BS)

2.3.Reconfigurable systems, design of system configurations (PhD, MS, BS)

2.4.Analysis, design, evolution of system requirements and standards (PhD, MS, BS)

III.Combinatorial Modeling in Life-cycle Engineering

3.1.Combinatorial modeling in requirements engineering (PhD, MS, BS)

3.2.Combinatorial modeling in maintenance (PhD, MS, BS)

3.3.Multi-product systems and product families (PhD, MS, BS)

3.4.Combinatorial modeling in multi-function system testing (PhD, MS, BS)

3.5.Combinatorial modeling of system evolution/development and forecasting (PhD, MS, BS)

IV.Networking

4.1.Combinatorial schemes for design of multilayer network topology (PhD, MS, BS):

(i)k-connected topology,

(ii)allocation of cross-links and "bridges",

(iii)direct network formation, and

(iv)re-design/upgrade.

4.2.Testing, probing problems (PhD, MS, BS)

4.3.Combinatorial modeling and evolution/development of protocols (PhD, BS, MS)

4.4.Crucial nodes, links, and components

(from the mathematical viewpoint, from the engineering/applied viewpoint) (PhD, MS, BS)