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)