Time-inconsistent Planning: Simple Motivation Is Hard to Find

11/18/2019
by   Fedor V. Fomin, et al.
0

With the introduction of the graph-theoretic time-inconsistent planning model due to Kleinberg and Oren, it has been possible to investigate the computational complexity of how a task designer best can support a present-biased agent in completing the task. In this paper, we study the complexity of finding a choice reduction for the agent; that is, how to remove edges and vertices from the task graph such that a present-biased agent will remain motivated to reach his target even for a limited reward. While this problem is NP-complete in general, this is not necessarily true for instances which occur in practice, or for solutions which are of interest to task designers. For instance, a task designer may desire to find the best task graph which is not too complicated. We therefore investigate the problem of finding simple motivating subgraphs. These are structures where the agent will modify his plan at most k times along the way. We quantify this simplicity in the time-inconsistency model as a structural parameter: The number of branching vertices (vertices with out-degree at least 2) in a minimal motivating subgraph. Our results are as follows: We give a linear algorithm for finding an optimal motivating path, i.e. when k=0. On the negative side, we show that finding a simple motivating subgraph is NP-complete even if we allow only a single branching vertex — revealing that simple motivating subgraphs are indeed hard to find. However, we give a pseudo-polynomial algorithm for the case when k is fixed and edge weights are rationals, which might be a reasonable assumption in practice.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/07/2022

On Plane Subgraphs of Complete Topological Drawings

Topological drawings are representations of graphs in the plane, where v...
research
11/11/2018

Generating subgraphs in chordal graphs

A graph G is well-covered if all its maximal independent sets are of the...
research
09/07/2018

Top-k Overlapping Densest Subgraphs: Approximation and Complexity

A central problem in graph mining is finding dense subgraphs, with sever...
research
08/27/2018

Turning Cliques into Paths to Achieve Planarity

Motivated by hybrid graph representations, we introduce and study the fo...
research
06/24/2019

Finding Optimal Solutions With Neighborly Help

Can we efficiently compute optimal solutions to instances of a hard prob...
research
04/26/2018

Who witnesses The Witness? Finding witnesses in The Witness is hard and sometimes impossible

We analyze the computational complexity of the many types of pencil-and-...
research
09/19/2016

On the Phase Transition of Finding a Biclique in a larger Bipartite Graph

We report on the phase transition of finding a complete subgraph, of spe...

Please sign up or login with your details

Forgot password? Click here to reset