Celeste is PSPACE-hard

We investigate the complexity of the platform video game Celeste. We prove that navigating Celeste is PSPACE-hard in five different ways, corresponding to different subsets of the game mechanics. In particular, we prove the game PSPACE-hard even without player input.Comment: 15 pages, 13 figures. Presented at 23rd Thailand-Japan Conference on Discrete and Computational Geometry, Graphs, and Game

Improved Local Computation Algorithms for Constructing Spanners

A spanner of a graph is a subgraph that preserves lengths of shortest paths up to a multiplicative distortion. For every $k$, a spanner with size $O(n^{1+1/k})$ and stretch $(2k+1)$ can be constructed by a simple centralized greedy algorithm, and this is tight assuming Erd\H{o}s girth conjecture. In this paper we study the problem of constructing spanners in a local manner, specifically in the Local Computation Model proposed by Rubinfeld et al. (ICS 2011). We provide a randomized Local Computation Agorithm (LCA) for constructing $(2r-1)$-spanners with $\tilde{O}(n^{1+1/r})$ edges and probe complexity of $\tilde{O}(n^{1-1/r})$ for $r \in \{2,3\}$, where $n$ denotes the number of vertices in the input graph. Up to polylogarithmic factors, in both cases, the stretch factor is optimal (for the respective number of edges). In addition, our probe complexity for $r=2$, i.e., for constructing a $3$-spanner, is optimal up to polylogarithmic factors. Our result improves over the probe complexity of Parter et al. (ITCS 2019) that is $\tilde{O}(n^{1-1/2r})$ for $r \in \{2,3\}$. Both our algorithms and the algorithms of Parter et al. use a combination of neighbor-probes and pair-probes in the above-mentioned LCAs. For general $k\geq 1$, we provide an LCA for constructing $O(k^2)$-spanners with $\tilde{O}(n^{1+1/k})$ edges using $O(n^{2/3}\Delta^2)$ neighbor-probes, improving over the $\tilde{O}(n^{2/3}\Delta^4)$ algorithm of Parter et al. By developing a new randomized LCA for graph decomposition, we further improve the probe complexity of the latter task to be $O(n^{2/3-(1.5-\alpha)/k}\Delta^2)$, for any constant $\alpha>0$. This latter LCA may be of independent interest.Comment: RANDOM 202

Flat Folding an Unassigned Single-Vertex Complex (Combinatorially Embedded Planar Graph with Specified Edge Lengths) without Flat Angles

A foundational result in origami mathematics is Kawasaki and Justin's simple, efficient characterization of flat foldability for unassigned single-vertex crease patterns (where each crease can fold mountain or valley) on flat material. This result was later generalized to cones of material, where the angles glued at the single vertex may not sum to $360^\circ$. Here we generalize these results to when the material forms a complex (instead of a manifold), and thus the angles are glued at the single vertex in the structure of an arbitrary planar graph (instead of a cycle). Like the earlier characterizations, we require all creases to fold mountain or valley, not remain unfolded flat; otherwise, the problem is known to be NP-complete (weakly for flat material and strongly for complexes). Equivalently, we efficiently characterize which combinatorially embedded planar graphs with prescribed edge lengths can fold flat, when all angles must be mountain or valley (not unfolded flat). Our algorithm runs in $O(n \log^3 n)$ time, improving on the previous best algorithm of $O(n^2 \log n)$.Comment: 17 pages, 8 figures, to appear in Proceedings of the 38th International Symposium on Computational Geometr

Lower Bounds on Retroactive Data Structures

We prove essentially optimal fine-grained lower bounds on the gap between a data structure and a partially retroactive version of the same data structure. Precisely, assuming any one of three standard conjectures, we describe a problem that has a data structure where operations run in O(T(n,m)) time per operation, but any partially retroactive version of that data structure requires T(n,m)?m^{1-o(1)} worst-case time per operation, where n is the size of the data structure at any time and m is the number of operations. Any data structure with operations running in O(T(n,m)) time per operation can be converted (via the "rollback method") into a partially retroactive data structure running in O(T(n,m)?m) time per operation, so our lower bound is tight up to an m^o(1) factor common in fine-grained complexity

This Game Is Not Going To Analyze Itself

We analyze the puzzle video game This Game Is Not Going To Load Itself, where the player routes data packets of three different colors from given sources to given sinks of the correct color. Given the sources, sinks, and some previously placed arrow tiles, we prove that the game is in Sigma_2^P; in NP for sources of equal period; NP-complete for three colors and six equal-period sources with player input; and even without player input, simulating the game is both NP- and coNP-hard for two colors and many sources with different periods. On the other hand, we characterize which locations for three data sinks admit a perfect placement of arrow tiles that guarantee correct routing no matter the placement of the data sources, effectively solving most instances of the game as it is normally played.Comment: 23 pages, 23 figures. Presented at JCDCGGG 202

The Student Movement Volume 108 Issue 6: Tayloring the Future: Andrews Inaugurates New President

HUMANS Filipino Pride and the Bayanihan Spirit, Savannah Tyler Intangible Impressions of Spiritual Life at Andrews, Savannah Tyler Meet the Majors: Part 2, Reagan McCain From Underdog to gRad-dog: A graduate student\u27s perspective on the transition from undergraduate to graduate school, Anna Rybachek ARTS & ENTERTAINMENT A New Chapter in Seasons, Nailea Soto A Report on the Eras Tour Movie, Nate Miller Gilmore Girls: The Downfall of College Rory, Audrey Lim How to Enter Music Circles on Campus, Reagan McCain NEWS Armenia - Azerbaijan Conflict, Katie Davis The Inauguration, Kiheon Chung Noche Latina: A Night to Celebrate Hispanic Heritage, Melissa Moore Understanding Tomorrow Today: The Fall 2023 Kingman Lecture, Jonathan Clough IDEAS My Struggle with Secular Music, Kiheon Chung No News Is Good News - But Here\u27s Some Good News!, Reagan Westerman Pakistan\u27s First Miss Universe Winner, Katie Davis PULSE American Melodies in Harmony with the AUSO, Aiko J. Ayala Rios Celebrating Filipino American History Month, Brooklyn Anderson Why We Can\u27t Seem to Get Enough Sleep, Alyssa Caruthers LAST WORD Do it For The Plot, Lily Burkehttps://digitalcommons.andrews.edu/sm-108/1005/thumbnail.jp

The Student Movement Volume 108 Issue 10: VP or Not VP?: That is the Question

HUMANS Interview with Dr. Ponce-Rodas: Change within the Church, Grace No Dean Spotlight Interview: Alyssa Palmer, Lauren Kim Maya Sukumaran\u27s Exploration: Unraveling the Neurobiology of Cricket Behavior, Nick Bishop ARTS & ENTERTAINMENT AUSO\u27s Vienna Classics Concert, Nate Miller Discovering the Fine Arts Program, Amelia Stefanescu What Do Murder and Law School Have in Common?, Amelia Stefanescu NEWS AU Abroad, Katie Davis Context, Changes, Reactions, What\u27s Coming, VP to the Assistant to the President, Lily Burke Founding of Andrews University, Kiheon Chung Israel-Gaza Follow Up, Robert Zhang Second Annual AU Shark Tank Features Intriguing Proposals, Andrew Francis IDEAS Coming Out Ministries in Berrien Springs, Erin Beers How to Spread Holiday Cheer on a Budget!, Reagan Westerman Rabbit Rabbit, Katie Davis What is Truth? My Personal Exploration into Moral Relativism, Bella Hamann PULSE A Taste of Goodness, Anna Rybachek Countdown to Finals: Tips for Test-Taking, Sumin Lee Why Andrews?, Alyssa Caruthers LAST WORD My Semester of Touching Grass and Smelling the Roses, Grace Nohttps://digitalcommons.andrews.edu/sm-108/1009/thumbnail.jp