Feodor F. Dragan
Sponsored Links
This presentation is the property of its rightful owner.
1 / 14

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


  • 83 Views
  • Uploaded on
  • Presentation posted in: General

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.

Download Presentation

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

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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

  • 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

  • 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.


  • 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


    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 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.


    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 PolygonsMethod


    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)


    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 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 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.


    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


    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


  • Login