| Research Abstract |
Purposes : Research on designing efficient algorithms for finding optimum solutions or sharp approximate ones to the network optimization problems.
Research results : They are divided into the following categories.
(1) Constructing survivable networks : Algorithms for finding optimum or approximate solutions to the connectivity augmentation problems are proposed, where designing networks that survive link or node faults is modeled as the connectivity augmentation problems. The following problems are considered. (i) K-edge-connectivity augmentation problems without creating multiple edges of a graph; (ii) K-edge-connectivity augmentation problems with upper bounds on edge multiplicity; (iii) Distributed algorithms for the k-edge-connectivity augmentation problems; (iv) Approximation algorithms for the Steiner tree problem of hypergraphs.
(2) Fundamental research on design and verification of communication protocols : Efficient algorithms for obtaining siphons or invariants of Petri nets ar
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e proposed, where verification or periodicity of communication protocols, respectively, is closely related to siphons or invariants or Petri nets that are used in modeling. The following problems are considered. (i) Extraction of minimal siphons; (ii) Computation of minimal support invariants.
(3) Solving scheduling problems : Scheduling problems are modeled as finding legal firing sequences in ordinary or timed Petri nets, and efficient heuristic algorithms are proposed.
(4) Designing printed wiring boards : Efficient heuristic algorithms for several fundamental problems in designing printed wiring boards are proposed. The following problems are considered. (i) Extracting spanning planar subgraphs; (ii) Routing problems; (iii) Constrained via minimization problems.
(5) Graph drawing : Efficient algorithms for drawing graphs on a given surface are proposed, where many practical constraints on graph drawing, such as minimizing total length or crossing of lines, specifying crossing points of certain lines, and so on, are satisfied.
(6) Others : A book entitled "Data Structures and Fundamental Algorithms" on design and analysis of algorithms is published, where basic concepts are explained in great detail by using many figures. Less
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