A Survey of Tree Convex Sets Test

TL;DR

This paper reviews key materials for a linear recognition algorithm of tree convex sets, which are collections of sets forming subtrees in a tree, with applications in solving certain constraint satisfaction and auction problems.

Contribution

It provides a comprehensive review of the foundational materials necessary for developing a linear recognition algorithm for tree convex sets.

Findings

Identifies key materials for recognition algorithm

Highlights applications in CSPs and auctions

Discusses recent polynomial algorithms

Abstract

Tree convex sets refer to a collection of sets such that each set in the collection is a subtree of a tree whose nodes are the elements of these sets. They extend the concept of row convex sets each of which is an interval over a total ordering of the elements of those sets. They have been applied to identify tractable Constraint Satisfaction Problems and Combinatorial Auction Problems. Recently, polynomial algorithms have been proposed to recognize tree convex sets. In this paper, we review the materials that are the key to a linear recognition algorithm.