Difference between revisions of "Open Problems:97"

From Open Problems in Sublinear Algorithms
Jump to: navigation, search
(Created page with "{{Header |title=Local Computation Algorithm for MIS |source=wola19 |who=Mohsen Gaffhari }} In the model of Local Computation Algorithms (LCA), given an input graph $G=(V,E)$,...")
 
m (Updating the header)
Line 1: Line 1:
 
{{Header
 
{{Header
|title=Local Computation Algorithm for MIS
 
 
|source=wola19
 
|source=wola19
 
|who=Mohsen Gaffhari
 
|who=Mohsen Gaffhari
 
}}
 
}}
 
 
In the model of Local Computation Algorithms (LCA), given an input graph $G=(V,E)$, an algorithm gets, upon query any vertex $v$ of its choosing, the list of neighbors of $v$. In this model, the current state-of-the-art for the query complexity of computing a Maximal Independent Set (MIS) for graph $G$ of maximum degree at most $\Delta$ is an upper bound of  
 
In the model of Local Computation Algorithms (LCA), given an input graph $G=(V,E)$, an algorithm gets, upon query any vertex $v$ of its choosing, the list of neighbors of $v$. In this model, the current state-of-the-art for the query complexity of computing a Maximal Independent Set (MIS) for graph $G$ of maximum degree at most $\Delta$ is an upper bound of  
 
$$
 
$$

Revision as of 18:16, 26 August 2019

Suggested by Mohsen Gaffhari
Source WOLA 2019
Short link https://sublinear.info/97

In the model of Local Computation Algorithms (LCA), given an input graph $G=(V,E)$, an algorithm gets, upon query any vertex $v$ of its choosing, the list of neighbors of $v$. In this model, the current state-of-the-art for the query complexity of computing a Maximal Independent Set (MIS) for graph $G$ of maximum degree at most $\Delta$ is an upper bound of $$ \Delta^{O(\log\log \Delta)} \operatorname{poly}\!\log n $$ queries.

Question: Does there exist a $\operatorname{poly}(\log n, \Delta)$-query LCA for MIS?