RESEARCH TOPICS FOR STUDENTS (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 engineering (technological) systems problems (PhD, MS, BS):

(i) hierarchical modeling of composite (modular) system,

(ii) system design,

(iii) system evaluation,

(iv) detection of system bottlenecks,

(v) redesign/improvement/adaptation of system,

(vi) multistage system design or design of system trajectory, and

(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) redesign/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)