On the complexity of the (approximate) nearest colored node problem

07/10/2018
by   Maximilian Probst, et al.
0

Given a graph G=(V,E) where each vertex is assigned a color from the set C={c_1, c_2, .., c_σ}. In the (approximate) nearest colored node problem, we want to query, given v ∈ V and c ∈ C, for the (approximate) distance dist(v, c) from v to the nearest node of color c. For any integer 1 ≤ k ≤ n, we present a Color Distance Oracle (also often referred to as Vertex-label Distance Oracle) of stretch 4k-5 using space O(knσ^1/k) and query time O(k). This improves the query time from O(k) to O(k) over the best known Color Distance Oracle by Chechik DBLP:journals/corr/abs-1109-3114. We then prove a lower bound in the cell probe model showing that our query time is optimal in regard to space up to constant factors. We also investigate dynamic settings of the problem and find new upper and lower bounds.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/05/2018

Almost Optimal Distance Oracles for Planar Graphs

We present new tradeoffs between space and query-time for exact distance...
research
09/30/2021

Near-Optimal Distance Oracles for Vertex-Labeled Planar Graphs

Given an undirected n-vertex planar graph G=(V,E,ω) with non-negative ed...
research
02/06/2019

QMA Lower Bounds for Approximate Counting

We prove a query complexity lower bound for QMA protocols that solve app...
research
03/19/2018

Exact Distance Oracles Using Hopsets

For fixed h ≥ 2, we consider the task of adding to a graph G a set of we...
research
07/14/2022

A Query-Optimal Algorithm for Finding Counterfactuals

We design an algorithm for finding counterfactuals with strong theoretic...
research
05/22/2023

Error-Tolerant Exact Query Learning of Finite Set Partitions with Same-Cluster Oracle

This paper initiates the study of active learning for exact recovery of ...
research
11/05/2021

Maintaining Exact Distances under Multiple Edge Failures

We present the first compact distance oracle that tolerates multiple fai...

Please sign up or login with your details

Forgot password? Click here to reset