The Complexity of Node Blocking for Dags

TL;DR

This paper analyzes the computational complexity of a node blocking game on directed acyclic graphs, proving that determining a winning strategy is PSPACE-complete, highlighting the game's inherent difficulty.

Contribution

The paper introduces the node blocking game on DAGs and establishes its PSPACE-completeness, a novel complexity result for this type of game.

Findings

Determined the game is PSPACE-complete.

Established complexity for arbitrary configurations.

Contributed to understanding of game complexity on DAGs.

Abstract

We consider the following modification of annihilation game called node blocking. Given a directed graph, each vertex can be occupied by at most one token. There are two types of tokens, each player can move his type of tokens. The players alternate their moves and the current player $i$ selects one token of type $i$ and moves the token along a directed edge to an unoccupied vertex. If a player cannot make a move then he loses. We consider the problem of determining the complexity of the game: given an arbitrary configuration of tokens in a directed acyclic graph, does the current player has a winning strategy? We prove that the problem is PSPACE-complete.