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Exponential Speed-Up of Local Algorithms using Non-Local Communication

Explore the potential speed increase in distributed systems by incorporating "non-local" communication, abstracting the classical local model. Investigate the benefits of combining local and non-local communication in communication models where |V| = n nodes with limitations on bandwidth and memory. Tasks such as solving graph problems on G = (V,E) with maximum degree ¢ of G and exploring concepts like MIS, MDS, max matching, and coloring. Collecting entire multi-hop neighborhoods in G to simulate multiple rounds of local algorithm in one. The theorem states that any local algorithm terminating within r^2O(log n) rounds can be simulated within O(log r) rounds when input size is at most n²/2. Examples included.

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Exponential Speed-Up of Local Algorithms using Non-Local Communication

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  1. Exponential Speed-Up of Local Algorithms using Non-Local Communication

  2. distributed systems with "non-local" communication abstracting communication "classical" local model

  3. Local vs. Non-Local Communication Can we combine it?

  4. Model Communication: |V| =n nodes that may exchange messages directly bandwidth and memory limitation of n² (² constant) Task: graph problem on G = (V,E) maximum degree ¢ of G polylogarithmic nodes know neighbors in G MIS, MDS, max. matching, coloring, etc. large degrees implied small diameter anyway

  5. Idea collect entire (multi-hop) neighorhoods in G distance to which graph is known grows exponentially simulate multiple rounds of local algorithm in one v

  6. Results Theorem: Given that inputs are of size at most n²/2, any local algorithm terminating within r2O(log n) rounds can be simulated within O(log r) rounds.

  7. Examples

  8. Thank You!Questions & Comments? TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAA

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