Locality of Distributed Graph Problems

distributed algorithms;local model;locally checkable labeling;coloring;Computer Science;Engineering;Computer Science & Engineering

Chang, Yi-JunSuomela, Jukka ;

University of Michigan

关键词: distributed algorithms;    local model;    locally checkable labeling;    coloring;    Computer Science;    Engineering;    Computer Science & Engineering;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/149872/cyijun_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Locality is one of the central themes in distributed computing. Suppose in a network each node only has direct communication with its local neighbors, how efficiently can a global task be solved? We aim to investigate the locality of fundamental distributed graph problems. Toward this goal, we consider the following three basic abstract models of distributed computing.• LOCAL: each device has direct communication links with its neighbors, there is no message size constraint.• CONGEST: each device has direct communication links with its neighbors, the size of each message is at most O(log n) bits.• CONGESTED-CLIQUE: each device has direct communication links with all other devices, the size of each message is at most O(log n) bits.A brief summary of our results is as follows.1. Complexity Theory for the LOCAL Model: We study the spectrum of natural problem complexities that can exist in the LOCAL model. We provide answers to the following fundamental questions regarding the nature of the LOCAL model: (i) How to classify the distributed problems according to their complexities? (ii) How much does randomness help? (iii) Can we solve more problems given more time?2. Complexity of Distributed Coloring: The coloring problem is a classical and well-studied problem in distributed computing. We devise distributed algorithms for the edge-coloring problem and the vertex-coloring problem in the LOCAL model that improve upon the previous state of the art.3. Bandwidth Constraint: We develop a new framework for algorithm design based on expander decompositions that allows us to apply CONGESTED-CLIQUE techniques to the CONGEST model. Using this approach, we provide improved algorithms for the triangle detection and enumeration problem in CONGEST.