Planning over Chain Causal Graphs for Variables with Domains of Size 5 Is NP-Hard

01/15/2014
by   Omer Giménez, et al.
0

Recently, considerable focus has been given to the problem of determining the boundary between tractable and intractable planning problems. In this paper, we study the complexity of planning in the class C_n of planning problems, characterized by unary operators and directed path causal graphs. Although this is one of the simplest forms of causal graphs a planning problem can have, we show that planning is intractable for C_n (unless P = NP), even if the domains of state variables have bounded size. In particular, we show that plan existence for C_n^k is NP-hard for k>=5 by reduction from CNFSAT. Here, k denotes the upper bound on the size of the state variable domains. Our result reduces the complexity gap for the class C_n^k to cases k=3 and k=4 only, since C_n^2 is known to be tractable.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/31/2011

The Complexity of Planning Problems With Simple Causal Graphs

We present three new complexity results for classes of planning problems...
research
02/04/2014

A Refined View of Causal Graphs and Component Sizes: SP-Closed Graph Classes and Beyond

The causal graph of a planning instance is an important tool for plannin...
research
06/26/2011

Structure and Complexity in Planning with Unary Operators

Unary operator domains -- i.e., domains in which operators have a single...
research
10/02/2018

Contracting to a Longest Path in H-Free Graphs

We prove two dichotomy results for detecting long paths as patterns in a...
research
02/06/2013

The Complexity of Plan Existence and Evaluation in Probabilistic Domains

We examine the computational complexity of testing and finding small pla...
research
09/26/2019

Causal Belief Decomposition for Planning with Sensing: Completeness Results and Practical Approximation

Belief tracking is a basic problem in planning with sensing. While the p...
research
09/10/2018

Complexity of Timeline-Based Planning over Dense Temporal Domains: Exploring the Middle Ground

In this paper, we address complexity issues for timeline-based planning ...

Please sign up or login with your details

Forgot password? Click here to reset