Price Query: Difference between revisions
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(Created page with "{{DISPLAYTITLE:Price Query (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”...") |
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== Parameters == | == Parameters == | ||
n: number of vertices | |||
m: number of edges | |||
m: number of edges | |||
== Table of Algorithms == | == Table of Algorithms == | ||
Revision as of 12:04, 15 February 2023
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 |