On One-Round Discrete Voronoi Games

Let V be a multiset of n points in R^d, which we call voters, and let k >=slant 1 and l >=slant 1 be two given constants. We consider the following game, where two players P and Q compete over the voters in V: First, player P selects a set P of k points in R^d, and then player Q selects a set Q of l points in R^d. Player P wins a voter v in V iff dist(v,P) <=slant dist(v,Q), where dist(v,P) := min_{p in P} dist(v,p) and dist(v,Q) is defined similarly. Player P wins the game if he wins at least half the voters. The algorithmic problem we study is the following: given V, k, and l, how efficiently can we decide if player P has a winning strategy, that is, if P can select his k points such that he wins the game no matter where Q places her points. Banik et al. devised a singly-exponential algorithm for the game in R^1, for the case k=l. We improve their result by presenting the first polynomial-time algorithm for the game in R^1. Our algorithm can handle arbitrary values of k and l. We also show that if d >= 2, deciding if player P has a winning strategy is Sigma_2^P-hard when k and l are part of the input. Finally, we prove that for any dimension d, the problem is contained in the complexity class exists for all R, and we give an algorithm that works in polynomial time for fixed k and l

The Complexity of Recognizing Geometric Hypergraphs

As set systems, hypergraphs are omnipresent and have various representations ranging from Euler and Venn diagrams to contact representations. In a geometric representation of a hypergraph $H=(V,E)$, each vertex $v\in V$ is associated with a point $p_v\in \mathbb{R}^d$ and each hyperedge $e\in E$ is associated with a connected set $s_e\subset \mathbb{R}^d$ such that $\{p_v\mid v\in V\}\cap s_e=\{p_v\mid v\in e\}$ for all $e\in E$. We say that a given hypergraph $H$ is representable by some (infinite) family $F$ of sets in $\mathbb{R}^d$, if there exist $P\subset \mathbb{R}^d$ and $S \subseteq F$ such that $(P,S)$ is a geometric representation of $H$. For a family F, we define RECOGNITION(F) as the problem to determine if a given hypergraph is representable by F. It is known that the RECOGNITION problem is $\exists\mathbb{R}$-hard for halfspaces in $\mathbb{R}^d$. We study the families of translates of balls and ellipsoids in $\mathbb{R}^d$, as well as of other convex sets, and show that their RECOGNITION problems are also $\exists\mathbb{R}$-complete. This means that these recognition problems are equivalent to deciding whether a multivariate system of polynomial equations with integer coefficients has a real solution.Comment: Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023) 17 pages, 11 figure

The Complexity of Recognizing Geometric Hypergraphs

As set systems, hypergraphs are omnipresent and have various representations. In a geometric representation of a hypergraph H=(V,E), each vertex v∈V is a associated with a point pv∈Rd and each hyperedge e∈E is associated with a connected set se⊂Rd such that {pv∣v∈V}∩se={pv∣v∈e} for all e∈E. We say that a given hypergraph H is representable by some (infinite) family F of sets in Rd, if there exist P⊂Rd and S⊆F such that (P,S) is a geometric representation of H. For a family F, we define RECOGNITION(F) as the problem to determine if a given hypergraph is representable by F. It is known that the RECOGNITION problem is ER-hard for halfspaces in Rd. We study the families of balls and ellipsoids in Rd, as well as other convex sets, and show that their RECOGNITION problems are also ER-complete. This means that these recognition problems are equivalent to deciding whether a multivariate system of polynomial equations with integer coefficients has a real solution

Reinforcement Learning for Generative Art

Reinforcement learning (RL) is an efficient class of sequential decision-making algorithms that have achieved remarkable success in a broad range of applications, such as robotic manipulations, strategic games, or autonomous driving. The most well-known example of reinforcement learning is AlphaGo, a computer program that plays the board game Go and outperforms top human Go players. Unlike other two major machine learning categories, supervised learning and unsupervised learning, in which media artists are actively engaged, reinforcement learning has yet to result in many creative applications. Generative art is usually driven, in whole or in part, by autonomous systems that are derived from a set of rules. Interestingly, an RL policy can be seen as an autonomous system where the rules are learned by interacting with its environment. Regardless of its initial purpose, reinforcement learning has the potential to expand the boundary of generative art. However, a formal process of applying reinforcement learning to generative art does not yet exist and the current RL tools require an in-depth understanding of RL concepts. To bridge the gap, the first part of the dissertation introduces a conceptual framework to adapt reinforcement learning for generative art. The framework proposes a term RL-based generative art to denote a novel form of generative art of which the use of RL agents is the key element. The creative process of RL-based generative art and possible emergent behaviors are discussed in the framework. This leads to a discussion of several author's related practices on generative art, deep-learning art, and reinforcement learning. Those practices are critical for understanding the conceptual and technical details of each component in order to construct the framework. The second part introduces RL5, a JavaScript library for rapidly prototyping RL environments and training RL policies in web browsers. The library combines RL algorithms and RL environments into one framework and is fully compatible with p5.js. RL5 is developed with a particular focus on simplicity to favor (re)usability of RL algorithms and development of RL environments. Specifically, the library implemented three RL algorithms, Tabular Q-learning, REINFORCE, and DDPG, to cover all the three families of model-free RL, and nine RL environments that six of them address autonomous agents in steering behaviors, which can be used as building blocks for complex systems. Finally, the author demonstrates four different use cases of how to apply RL5 for pedagogical and creative applications

Proceedings of the SAB'06 Workshop on Adaptive Approaches for Optimizing Player Satisfaction in Computer and Physical Games

These proceedings contain the papers presented at the Workshop on Adaptive approaches for Optimizing Player Satisfaction in Computer and Physical Games held at the Ninth international conference on the Simulation of Adaptive Behavior (SAB’06): From Animals to Animats 9 in Rome, Italy on 1 October 2006. We were motivated by the current state-of-the-art in intelligent game design using adaptive approaches. Artificial Intelligence (AI) techniques are mainly focused on generating human-like and intelligent character behaviors. Meanwhile there is generally little further analysis of whether these behaviors contribute to the satisfaction of the player. The implicit hypothesis motivating this research is that intelligent opponent behaviors enable the player to gain more satisfaction from the game. This hypothesis may well be true; however, since no notion of entertainment or enjoyment is explicitly defined, there is therefore little evidence that a specific character behavior generates enjoyable games. Our objective for holding this workshop was to encourage the study, development, integration, and evaluation of adaptive methodologies based on richer forms of humanmachine interaction for augmenting gameplay experiences for the player. We wanted to encourage a dialogue among researchers in AI, human-computer interaction and psychology disciplines who investigate dissimilar methodologies for improving gameplay experiences. We expected that this workshop would yield an understanding of state-ofthe- art approaches for capturing and augmenting player satisfaction in interactive systems such as computer games. Our invited speaker was Hakon Steinø, Technical Producer of IO-Interactive, who discussed applied AI research at IO-Interactive, portrayed the future trends of AI in computer game industry and debated the use of academic-oriented methodologies for augmenting player satisfaction. The sessions of presentations and discussions where classified into three themes: Adaptive Learning, Examples of Adaptive Games and Player Modeling. The Workshop Committee did a great job in providing suggestions and informative reviews for the submissions; thank you! This workshop was in part supported by the Danish National Research Council (project no: 274-05-0511). Finally, thanks to all the participants; we hope you found this to be useful!peer-reviewe

Covering Problems via Structural Approaches

The minimum set cover problem is, without question, among the most ubiquitous and well-studied problems in computer science. Its theoretical hardness has been fully characterized--logarithmic approximability has been established, and no sublogarithmic approximation exists unless P=NP. However, the gap between real-world instances and the theoretical worst case is often immense--many covering problems of practical relevance admit much better approximations, or even solvability in polynomial time. Simple combinatorial or geometric structure can often be exploited to obtain improved algorithms on a problem-by-problem basis, but there is no general method of determining the extent to which this is possible. In this thesis, we aim to shed light on the relationship between the structure and the hardness of covering problems. We discuss several measures of structural complexity of set cover instances and prove new algorithmic and hardness results linking the approximability of a set cover problem to its underlying structure. In particular, we provide: - An APX-hardness proof for a wide family of problems that encode a simple covering problem known as Special-3SC. - A class of polynomial dynamic programming algorithms for a group of weighted geometric set cover problems having simple structure. - A simplified quasi-uniform sampling algorithm that yields improved approximations for weighted covering problems having low cell complexity or geometric union complexity. - Applications of the above to various capacitated covering problems via linear programming strengthening and rounding. In total, we obtain new results for dozens of covering problems exhibiting geometric or combinatorial structure. We tabulate these problems and classify them according to their approximability

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum