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The Next Talk Fa'16 Talks General Info Speaking Req't

Incremental Voronoi Diagrams

Monday, December 5th, 2016 from 12-1 pm in GHC 6501.

Sarah R. Allen, CSD

We study the amortized number of combinatorial changes (edge insertions and removals) needed to update the graph structure of the Voronoi diagram VD(S) (and several variants thereof) of a set S of n sites in the plane as sites are added to the set. To that effect, we define a general update operation for planar graphs that can be used to model the incremental construction of several variants of Voronoi diagrams as well as the incremental construction of an intersection of halfspaces in 3 Dimensional space. We show that the amortized number of edge insertions and removals needed to add a new site to the Voronoi diagram is O(sqrt{n}). A matching Omega(sqrt{n}) combinatorial lower bound is shown, even in the case where the graph representing the Voronoi diagram is a tree. This contrasts with the O(log n) upper bound of Aronov et al. (2006) for farthest-point Voronoi diagrams in the special case where the points are inserted in clockwise order along their convex hull.

We then present a semi-dynamic data structure that maintains the Voronoi diagram of a set S of n sites in convex position. This data structure supports the insertion of a new site p (and hence the addition of its Voronoi cell) and finds the asymptotically minimal number K of edge insertions and removals needed to obtain the diagram of S including p from the diagram of the original S, in time O(K polylog n) worst case, which is O(sqrt{n} ;polylog n) amortized by the aforementioned combinatorial result.

The most distinctive feature of this data structure is that the graph of the Voronoi diagram is maintained explicitly at all times and can be retrieved and traversed in the natural way; this contrasts with other structures supporting nearest neighbor queries in that they do not maintain the Voronoi diagram after each insertion. This structure supports general search operations on the current Voronoi diagram, which can, for example, be used to perform point location queries in the cells of the current Voronoi diagram in O(log n) time, or to determine whether two given sites are neighbors in the Delaunay triangulation

Joint work with Luis Barba, John Iacono, and Stefan Langerman

Presented in Partial Fulfillment of the CSD Speaking Skills Requirement.


Fall 2016 Schedule
Fri, Sep 2 GHC 4303 Expired
Fri, Sep 9 GHC 4303 Expired
Mon, Sep 12 GHC 6501 Expired
Fri, Sep 16 GHC 4303 Expired
Mon, Sep 19 GHC 6501 Expired
Fri, Sep 23 GHC 4303 Expired
Mon, Sep 26 GHC 6501 Zhou Yu Engagement in Interactive Multimodal Conversational System
Fri, Sep 30 GHC 4303 Expired
Mon, Oct 3 GHC 6501 Kuen-Bang Hou (Favonia) A Mechanization of the Blakers-Massey Connectivity Theorem in Homotopy Type Theory
Fri, Oct 7 GHC 4303 Expired
Mon, Oct 10 GHC 6501 Yuzuko Nakamura Factors affecting bimanual grasping
Fri, Oct 14 GHC 4303 Mu Li MXNet: Flexible Deep Learning Framework from Distributed GPU Clouds to Embedded Systems
Mon, Oct 17 GHC 6501 Tanmay Shankar Reinforcement Learning via Recurrent Convolutional Neural Networks
Fri, Oct 21 GHC 4303 Expired
Mon, Oct 24 GHC 6501 Expired
Fri, Oct 28 GHC 4303 Expired
Mon, Oct 31 GHC 6501 Expired
Fri, Nov 4 GHC 4303 Expired
Mon, Nov 7 GHC 6501 Expired
Fri, Nov 11 GHC 4303 Expired
Mon, Nov 14 GHC 6501 Wennie Tabib Active Exploration in 3D-rich Planetary Environments
Fri, Nov 18 GHC 4303 Expired
Mon, Nov 21 GHC 6501 Alejandro Carbonara A Game Theoretic Treatment of Peer Grading in MOOCs
Fri, Nov 25 GHC 4303 Thanksgiving UNAVAILABLE
Mon, Nov 28 GHC 6501 AVAILABLE
Fri, Dec 2 GHC 4303 AVAILABLE
Mon, Dec 5 GHC 6501 Sarah R. Allen Incremental Voronoi Diagrams
Fri, Dec 9 GHC 4303 Yihan Sun Just Join for Parallel Ordered Sets
Mon, Dec 12 GHC 6501 AVAILABLE


General Info

The Student Seminar Series is an informal research seminar by and for SCS graduate students from noon to 1 pm on Mondays and Fridays. Lunch is provided by the Computer Science Department (personal thanks to Sharon Burks and Debbie Cavlovich!). At each meeting, a different student speaker will give an informal, 40-minute talk about his/her research, followed by questions/suggestions/brainstorming. We try to attract people with a diverse set of interests, and encourage speakers to present at a very general, accessible level.

So why are we doing this and why take part? In the best case scenario, this will lead to some interesting cross-disciplinary work among people in different fields and people may get some new ideas about their research. In the worst case scenario, a few people will practice their public speaking and the rest get together for a free lunch.


Guideline & Speaking Requirement Need-to-Know

Note: Step #1 below are applicable to all SSS speakers. You can schedule AT MOST THREE talks per semester.

SSS is an ideal forum for SCS students to give presentations that count toward fulfilling their speaking requirements. The specifics, though, vary with each department. For instance, students in CSD will need to be familiar with the notes in Section 8 of the Ph.D. document and follow the instructions outlined on the Speakers Club homepage. Roughly speaking, these are the steps:

  1. Schedule a talk with SSS by sending your talk title, abstract, additional info (like "Joint work with..." or "In Partial Fulfillment of the Speaking Requirement"), and a picture of yourself (preferably jpeg) to sss@cs at least TWO WEEKS before your scheduled talk.
  2. After you are confirmed with your SSS slot, go to the Speakers Club Calendar and schedule your talk at least THREE WEEKS in advance of the talk date.
  3. On the day of your talk, make sure you print Speakers Club evaluation forms for your evaluators to use.
Students outside of CSD will need to check with their respective departments regarding the procedure. As another example, ISRI students fulfill their speaking requirements by attending a semesterly Software Research Seminar and giving X number of presentations per school year. If you have experience with your department that might help others in your department, please feel free to contribute your knowledge by emailing us. Thank you!


SSS Coordinators

Armaghan Naik, Computational Biology
Lin Xiao, CSD

 


Web contact: sss+www@cs