Feodor F. Dragan
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Feodor F. Dragan 1990 Ph.D. in Theoretical Computer Science Institute of Mathematics of the Byelorussian Academy of Science, Minsk. Moldova State University (1988 – 1996) University of Duisburg (1994 – 1995) University of Rostock (1996 – 1999) UCLA (1999 – 2000) ???. Research interests.

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Moldova State University (1988 – 1996) University of Duisburg (1994 – 1995)

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Moldova state university 1988 1996 university of duisburg 1994 1995

Feodor F. Dragan1990 Ph.D. in Theoretical Computer ScienceInstitute of Mathematics of the Byelorussian Academy of Science, Minsk

  • Moldova State University (1988 – 1996)

  • University of Duisburg (1994 – 1995)

  • University of Rostock (1996 – 1999)

  • UCLA (1999 – 2000)

  • ???


Research interests

Research interests

  • Design and analysis of algorithms

  • Algorithmic graph and hypergraph theory

  • Computational geometry

  • Facility location problems

  • Operations research

  • Combinatorial optimization

  • VLSI CAD

  • Data analysis

  • Computational biology

  • Discrete convexity and geometry of discrete metric spaces


Efficient algorithms for some optimization problems

Efficient algorithms for some optimization problems

  • Median Points of Simple Rectilinear Polygons

  • A Link Central Point and the Link Diameter of a Simple Rectilinear Polygon

    • Computational geometry

    • Facility location problems

    • Operations research

    • Design and analysis of algorithms

    • Discrete convexity and geometry of discrete metric spaces.

  • Distance Approximating Trees in Graphs

    • Algorithmic graph theory

    • Data analysis

    • Networks design

    • etc.


  • Median points of simple rectilinear polygons chepoi dragan location science 1996

    Simple rectilinear polygon, vertices, edges

    Rectilinear path in P

    Length of the path

    - metric d(x,y) in P

    Median Points of Simple Rectilinear PolygonsChepoi & Dragan,Location Science, 1996


    Median points of simple rectilinear polygons

    number of users located at a point

    Weber Function

    is a median point if

    Med(P)

    Median Points of Simple Rectilinear Polygons


    Median points of simple rectilinear polygons1

    Median Points of Simple Rectilinear Polygons

    • Problem formulation (facility location problem)

      • Given P,

      • Find Med(P)

    • Algorithmic results

      • Med(P) can be found in O(nlogN + N) time.

      • If all users are located on vertices of P then in O(N + n) time.


    Median points of simple rectilinear polygons2

    Theoretical results used

    (P,d) is a median space

    Any convex compact subset of a median space is gated

    Med(P) is convex and forms a simple rectilinear polygon inside of P

    Majority role

    etc. etc. etc.

    Median Points of Simple Rectilinear Polygons


    Median points of simple rectilinear polygons method

    Median Points of Simple Rectilinear PolygonsMethod


    Moldova state university 1988 1996 university of duisburg 1994 1995

    A link central point and the link diameter of a simple rectilinear polygonChepoi & Dragan,Comput. Sci. J. of Moldova, `93; Russian J. of Oper. Res., `94

    • Link-distance in general polygons (Suri. PhD th. `87, motivated by robot motion-planning and broadcasting problems)

      • Minimum number of line segments/ of turns the path makes

    • Rectilinear/orthogonal link-distance in rectilinear polygons (M. de Berg `91)


    A link central point and the link diameter of a simple rectilinear polygon

    Eccentricity Function

    is a central point if

    is the minimum eccentricity of a point in P.

    is the maximum eccentricity of a point in P.

    C(P)

    A link central point and the link diameter of a simple rectilinear polygon


    A link central point and the link diameter of a simple rectilinear polygon1

    A link central point and the link diameter of a simple rectilinear polygon

    • Problem formulation (facility location problem)

      • Given P

      • Find C(P), rad(P), diam(P)

    • Previous results

      • In simple polygons

        • O(nlogn) for C(P) [Djidjev et al. `89],[Ke `89]

        • O(nlogn) for the diameter [Suri `87]

      • In simple rectilinear polygons

        • O(nlogn) for the diameter [de Berg `91]

        • Open for C(P)[de Berg `91]

    • Our algorithmic results

      • A link central point, the link radius, the link diameter of a simple rectilinear polygon can be found in O(n) time. (the same results were obtained independently by Nilsson & Schuierer in 1994 (1996); they used completely different approach)


    A link central point and the link diameter of a simple rectilinear polygon2

    A link central point and the link diameter of a simple rectilinear polygon

    • Theoretical results used

      • For any point x, the set of furthest points from x contains a vertex of P.

      • A pair of vertices with can be found in linear time.


    A link central point and the link diameter of a simple rectilinear polygon3

    Theoretical results used (c.)

    The center C(P) is not necessarily connected but forms an orthogonal convex set.

    diam(C(P)) <5

    The Helly property for intervals, etc., etc., etc.

    A link central point and the link diameter of a simple rectilinear polygon


    A link central point and the link diameter of a simple rectilinear polygon4

    Method

    eccentricity of a cut

    visibility intervals

    let

    Case 1.

    Case 2.

    or find instaircase,

    or repeat all for

    A link central point and the link diameter of a simple rectilinear polygon


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