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Title: | On the Probe Complexity of Local Computation Algorithms |
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Speaker: | Boaz Patt-Shamir |

coming from: | Max-Planck-Institut für Informatik - D1 |

Speakers Bio: | Boaz Patt-Shamir is a Professor of Computer Science in the School of Electrcal Engineering in Tel Aviv University since 1997, where he directs the laboratory for distributed algorithms. Prior to that, he was an assitant professor in Northeastern University in Boston. He received his BSc in Mathematics and Computer Science from Tel Aviv University, his MSc from Weizmann Institute, and his PhD from MIT.
His main research interest is network algorithms, including |

Event Type: | AG1 Mittagsseminar (others' work) |

Visibility: | D1 We use this to send out email in the morning. |

Level: | AG Audience |

Language: | English |

Date: | Tuesday, 12 March 2019 |
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Time: | 13:00 |

Duration: | 30 Minutes |

Location: | Saarbrücken |

Building: | E1 4 |

Room: | 024 |

In the Local Computation Algorithms (LCA) model, the algorithm is asked to compute a part of the output by reading as little as possible from the input. For example, an LCA for coloring a graph is given a vertex name (as a "query"), and it should output the color assigned to that vertex after inquiring about some part of the graph topology using "probes"; all outputs must be consistent with the same coloring. LCAs are useful when the input is huge, and the output as a whole is not needed simultaneously. Most previous work on LCAs was limited to bounded-degree graphs, which seems inevitable because probes are of the form "what vertex is at the other end of edge i of vertex v?". In this work we study LCAs for unbounded-degree graphs. In particular, such LCAs are expected to probe the graph a number of times that is significantly smaller than the maximum, average, or even minimum degree. We show that there are problems that have very efficient LCAs on any graph - specifically, we show that there is an LCA for the weak coloring problem (where a coloring is legal if every vertex has a neighbor with a different color) that uses log*n+O(1) probes to reply to any query. As another way of dealing with large degrees, we propose a more powerful type of probe which we call a *strong* probe: given a vertex name, it returns a list of its neighbors. Lower bounds for strong probes are stronger than ones in the edge probe model (which we call *weak* probes). Our main result in this model is that roughly Omega(sqrt(n)) strong probes are required to compute a maximal matching. Our findings include interesting separations between closely related problems. For weak probes, we show that while weak 3-coloring can be done with probe complexity log*n + O(1), weak 2-coloring has probe complexity Omega((log n)/loglog n). For strong probes, our negative result for *maximal* matching is complemented by an LCA for (1-epsilon)-approximate *maximum* matching on regular graphs that uses O(1) strong probes, for any constant epsilon>0. |

Name(s): | Christoph Lenzen |
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Video Broadcast: | No | To Location: |
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Note: | This is joint work with Uri Feige and Shai Vardi. |
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Attachments, File(s): |

Created: | Christoph Lenzen, 02/27/2019 05:52 PM |

Last modified: | Uwe Brahm/MPII/DE, 03/12/2019 04:01 AM |

- Christoph Lenzen, 02/27/2019 05:52 PM -- Created document.