Price Query

Description

For a graph with edge weight function $c : E \rightarrow Z$, a price query is an assignment of node weights $p : V \rightarrow Z$. Such a query has a yes answer if and only if there is a $(u,v) \in E$ such that $p(u) + p(v) > c(u,v)$. (Intuitively, the $p(v)$ are “prices” on the nodes, the $c(u,v)$ are costs of producing $u$ and $v$, and a price query asks if there is an edge we are willing to “sell” at the prices given by the query.)

Parameters

$n$: number of vertices

$m$: number of edges

Table of Algorithms

Currently no algorithms in our database for the given problem.

Reductions FROM Problem

Problem	Implication	Year	Citation	Reduction
Negative Triangle	if: to-time: $O(n^{2} / f(n))$ to answer any subsequent price query after $n$-node edge-weighted graph is preprocessed in $O(^k)$ time for some constant $k > {0}$ then: from-time: $O(n^{3} / f(n^{1/({2}k)})$	2018	https://dl.acm.org/doi/pdf/10.1145/3186893, Theorem 1.5	link