DeepAI AI Chat
Log In Sign Up

ARRIVAL: Next Stop in CLS

02/21/2018
by   Bernd Gärtner, et al.
0

We study the computational complexity of ARRIVAL, a zero-player game on n-vertex switch graphs introduced by Dohrau, Gärtner, Kohler, Matoušek, and Welzl. They showed that the problem of deciding termination of this game is contained in NP∩coNP. Karthik C. S. recently introduced a search variant of ARRIVAL and showed that it is in the complexity class PLS. In this work, we significantly improve the known upper bounds for both the decision and the search variants of ARRIVAL. First, we resolve a question suggested by Dohrau et al. and show that the decision variant of ARRIVAL is in UP∩coUP. Second, we prove that the search variant of ARRIVAL is contained in CLS. Third, we give a randomized O(1.4143^n)-time algorithm to solve both variants. Our main technical contributions are (a) an efficiently verifiable characterization of the unique witness for termination of the ARRIVAL game, and (b) an efficient way of sampling from the state space of the game. We show that the problem of finding the unique witness is contained in CLS, whereas it was previously conjectured to be FPSPACE-complete. The efficient sampling procedure yields the first algorithm for the problem that has expected runtime O(c^n) with c<2.

READ FULL TEXT

page 1

page 2

page 3

page 4

02/07/2022

Improved Bounds for Fractional Online Matching Problems

Online bipartite matching with one-sided arrival and its variants have b...
08/13/2021

A simple lower bound for ARRIVAL

The ARRIVIAL problem introduced by Dohrau, Gärtner, Kohler, Matoušek and...
02/25/2019

On One-Round Discrete Voronoi Games

Let V be a multiset of n points in R^d, which we call voters, and let k≥...
02/12/2021

A Subexponential Algorithm for ARRIVAL

The ARRIVAL problem is to decide the fate of a train moving along the ed...
11/23/2022

The Stochastic Arrival Problem

We study a new modification of the Arrival problem, which allows for nod...
04/27/2022

Polynomial Time Algorithm for ARRIVAL on Tree-like Multigraphs

A rotor walk in a directed graph can be thought of as a deterministic ve...
09/05/2022

Unique Sink Orientations of Grids is in Unique End of Potential Line

The complexity classes Unique End of Potential Line (UEOPL) and its prom...