**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)**