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Maximizing Phylogenetic Diversity under Ecological Constraints: A Parameterized Complexity Study 生态约束下的系统发育多样性最大化：参数化复杂性研究
arXiv - CS - Computational Complexity Pub Date : 2024-05-27 DOI: arxiv-2405.17314
Christian Komusiewicz, Jannik Schestag
{"title":"Maximizing Phylogenetic Diversity under Ecological Constraints: A Parameterized Complexity Study","authors":"Christian Komusiewicz, Jannik Schestag","doi":"arxiv-2405.17314","DOIUrl":"https://doi.org/arxiv-2405.17314","url":null,"abstract":"In the NP-hard Optimizing PD with Dependencies (PDD) problem, the input\u0000consists of a phylogenetic tree $T$ over a set of taxa $X$, a food-web that\u0000describes the prey-predator relationships in $X$, and integers $k$ and $D$. The\u0000task is to find a set $S$ of $k$ species that is viable in the food-web such\u0000that the subtree of $T$ obtained by retaining only the vertices of $S$ has\u0000total edge weight at least $D$. Herein, viable means that for every predator\u0000taxon of $S$, the set $S$ contains at least one prey taxon. We provide the\u0000first systematic analysis of PDD and its special case s-PDD from a\u0000parameterized complexity perspective. For solution-size related parameters, we\u0000show that PDD is FPT with respect to $D$ and with respect to $k$ plus the\u0000height of the phylogenetic tree. Moreover, we consider structural\u0000parameterizations of the food-web. For example, we show an FPT-algorithm for\u0000the parameter that measures the vertex deletion distance to graphs where every\u0000connected component is a complete graph. Finally, we show that s-PDD admits an\u0000FPT-algorithm for the treewidth of the food-web. This disproves a conjecture of\u0000Faller et al. [Annals of Combinatorics, 2011] who conjectured that s-PDD is\u0000NP-hard even when the food-web is a tree.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"81 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141165633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Maximal Line Digraphs 最大线段图
arXiv - CS - Computational Complexity Pub Date : 2024-05-27 DOI: arxiv-2406.05141
Quentin JaphetDAVID, Dimitri WatelIP Paris, SAMOVAR, SOP - SAMOVAR, ENSIIE, Dominique BarthDAVID, Marc-Antoine WeisserGALaC
{"title":"Maximal Line Digraphs","authors":"Quentin JaphetDAVID, Dimitri WatelIP Paris, SAMOVAR, SOP - SAMOVAR, ENSIIE, Dominique BarthDAVID, Marc-Antoine WeisserGALaC","doi":"arxiv-2406.05141","DOIUrl":"https://doi.org/arxiv-2406.05141","url":null,"abstract":"A line digraph $L(G) = (A, E)$ is the digraph constructed from the digraph $G\u0000= (V, A)$ such that there is an arc $(a,b)$ in $L(G)$ if the terminal node of\u0000$a$ in $G$ is the initial node of $b$. The maximum number of arcs in a line\u0000digraph with $m$ nodes is $(m/2)^2 + (m/2)$ if $m$ is even, and $((m - 1)/2)^2\u0000+ m - 1$ otherwise. For $m geq 7$, there is only one line digraph with as many\u0000arcs if $m$ is even, and if $m$ is odd, there are two line digraphs, each being\u0000the transpose of the other.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"207 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141518336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unconventional complexity classes in unconventional computing (extended abstract) 非常规计算中的非常规复杂性类别（扩展摘要）
arXiv - CS - Computational Complexity Pub Date : 2024-05-27 DOI: arxiv-2405.16896
Antonio E. Porreca
{"title":"Unconventional complexity classes in unconventional computing (extended abstract)","authors":"Antonio E. Porreca","doi":"arxiv-2405.16896","DOIUrl":"https://doi.org/arxiv-2405.16896","url":null,"abstract":"Many unconventional computing models, including some that appear to be quite\u0000different from traditional ones such as Turing machines, happen to characterise\u0000either the complexity class P or PSPACE when working in deterministic\u0000polynomial time (and in the maximally parallel way, where this applies). We\u0000discuss variants of cellular automata and membrane systems that escape this\u0000dichotomy and characterise intermediate complexity classes, usually defined in\u0000terms of Turing machines with oracles, as well as some possible reasons why\u0000this happens.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141165631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Strong Direct Sum Theorem for Distributional Query Complexity 分布式查询复杂性的强直接和定理
arXiv - CS - Computational Complexity Pub Date : 2024-05-25 DOI: arxiv-2405.16340
Guy Blanc, Caleb Koch, Carmen Strassle, Li-Yang Tan
{"title":"A Strong Direct Sum Theorem for Distributional Query Complexity","authors":"Guy Blanc, Caleb Koch, Carmen Strassle, Li-Yang Tan","doi":"arxiv-2405.16340","DOIUrl":"https://doi.org/arxiv-2405.16340","url":null,"abstract":"Consider the expected query complexity of computing the $k$-fold direct\u0000product $f^{otimes k}$ of a function $f$ to error $varepsilon$ with respect\u0000to a distribution $mu^k$. One strategy is to sequentially compute each of the\u0000$k$ copies to error $varepsilon/k$ with respect to $mu$ and apply the union\u0000bound. We prove a strong direct sum theorem showing that this naive strategy is\u0000essentially optimal. In particular, computing a direct product necessitates a\u0000blowup in both query complexity and error. Strong direct sum theorems contrast with results that only show a blowup in\u0000query complexity or error but not both. There has been a long line of such\u0000results for distributional query complexity, dating back to (Impagliazzo, Raz,\u0000Wigderson 1994) and (Nisan, Rudich, Saks 1994), but a strong direct sum theorem\u0000had been elusive. A key idea in our work is the first use of the Hardcore Theorem (Impagliazzo\u00001995) in the context of query complexity. We prove a new \"resilience lemma\"\u0000that accompanies it, showing that the hardcore of $f^{otimes k}$ is likely to\u0000remain dense under arbitrary partitions of the input space.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"345 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141165515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Complexity of Multiple-Hamiltonicity in Graphs of Bounded Degree 有界度图中多重哈密顿性的复杂性
arXiv - CS - Computational Complexity Pub Date : 2024-05-25 DOI: arxiv-2405.16270
Brian Liu, Nathan S. Sheffield, Alek Westover
{"title":"Complexity of Multiple-Hamiltonicity in Graphs of Bounded Degree","authors":"Brian Liu, Nathan S. Sheffield, Alek Westover","doi":"arxiv-2405.16270","DOIUrl":"https://doi.org/arxiv-2405.16270","url":null,"abstract":"We study the following generalization of the Hamiltonian cycle problem: Given\u0000integers $a,b$ and graph $G$, does there exist a closed walk in $G$ that visits\u0000every vertex at least $a$ times and at most $b$ times? Equivalently, does there\u0000exist a connected $[2a,2b]$ factor of $2b cdot G$ with all degrees even? This\u0000problem is NP-hard for any constants $1 leq a leq b$. However, the graphs\u0000produced by known reductions have maximum degree growing linearly in $b$. The\u0000case $a = b = 1 $ -- i.e. Hamiltonicity -- remains NP-hard even in $3$-regular\u0000graphs; a natural question is whether this is true for other $a$, $b$. In this work, we study which $a, b$ permit polynomial time algorithms and\u0000which lead to NP-hardness in graphs with constrained degrees. We give tight\u0000characterizations for regular graphs and graphs of bounded max-degree, both\u0000directed and undirected.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141165500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Game Derandomization 游戏去随机化
arXiv - CS - Computational Complexity Pub Date : 2024-05-25 DOI: arxiv-2405.16353
Samuel Epstein
{"title":"Game Derandomization","authors":"Samuel Epstein","doi":"arxiv-2405.16353","DOIUrl":"https://doi.org/arxiv-2405.16353","url":null,"abstract":"Using Kolmogorov Game Derandomization, upper bounds of the Kolmogorov\u0000complexity of deterministic winning players against deterministic environments\u0000can be proved. This paper gives improved upper bounds of the Kolmogorov\u0000complexity of such players. This paper also generalizes this result to\u0000probabilistic games. This applies to computable, lower computable, and\u0000uncomputable environments. We characterize the classic even-odds game and then\u0000generalize these results to time bounded players and also to all zero-sum\u0000repeated games. We characterize partial game derandomization. But first, we\u0000start with an illustrative example of game derandomization, taking place on the\u0000island of Crete.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141165501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Pseudorandomness, symmetry, smoothing: I 伪随机性、对称性、平滑性：I
arXiv - CS - Computational Complexity Pub Date : 2024-05-21 DOI: arxiv-2405.13143
Harm Derksen, Peter Ivanov, Chin Ho Lee, Emanuele Viola
{"title":"Pseudorandomness, symmetry, smoothing: I","authors":"Harm Derksen, Peter Ivanov, Chin Ho Lee, Emanuele Viola","doi":"arxiv-2405.13143","DOIUrl":"https://doi.org/arxiv-2405.13143","url":null,"abstract":"We prove several new results about bounded uniform and small-bias\u0000distributions. A main message is that, small-bias, even perturbed with noise,\u0000does not fool several classes of tests better than bounded uniformity. We prove\u0000this for threshold tests, small-space algorithms, and small-depth circuits. In\u0000particular, we obtain small-bias distributions that 1) achieve an optimal lower bound on their statistical distance to any\u0000bounded-uniform distribution. This closes a line of research initiated by Alon,\u0000Goldreich, and Mansour in 2003, and improves on a result by O'Donnell and Zhao. 2) have heavier tail mass than the uniform distribution. This answers a\u0000question posed by several researchers including Bun and Steinke. 3) rule out a popular paradigm for constructing pseudorandom generators,\u0000originating in a 1989 work by Ajtai and Wigderson. This again answers a\u0000question raised by several researchers. For branching programs, our result\u0000matches a bound by Forbes and Kelley. Our small-bias distributions above are symmetric. We show that the xor of any\u0000two symmetric small-bias distributions fools any bounded function. Hence our\u0000examples cannot be extended to the xor of two small-bias distributions, another\u0000popular paradigm whose power remains unknown. We also generalize and simplify\u0000the proof of a result of Bazzi.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fixed-parameter tractability of canonical polyadic decomposition over finite fields 有限域上典型多面体分解的固定参数可操作性
arXiv - CS - Computational Complexity Pub Date : 2024-05-19 DOI: arxiv-2405.11699
Jason Yang
{"title":"Fixed-parameter tractability of canonical polyadic decomposition over finite fields","authors":"Jason Yang","doi":"arxiv-2405.11699","DOIUrl":"https://doi.org/arxiv-2405.11699","url":null,"abstract":"We present a simple proof that finding a rank-$R$ canonical polyadic\u0000decomposition of 3-dimensional tensors over a finite field $mathbb{F}$ is\u0000fixed-parameter tractable with respect to $R$ and $mathbb{F}$. We also show\u0000some more concrete upper bounds on the time complexity of this problem.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Injective hardness condition for PCSPs PCSP 的注入硬度条件
arXiv - CS - Computational Complexity Pub Date : 2024-05-17 DOI: arxiv-2405.10774
Demian Banakh, Marcin Kozik
{"title":"Injective hardness condition for PCSPs","authors":"Demian Banakh, Marcin Kozik","doi":"arxiv-2405.10774","DOIUrl":"https://doi.org/arxiv-2405.10774","url":null,"abstract":"We present a template for the Promise Constraint Satisfaction Problem (PCSP)\u0000which is NP-hard but does not satisfy the current state-of-the-art hardness\u0000condition [ACMTCT'21]. We introduce a new \"injective\" condition based on the\u0000smooth version of the layered PCP Theorem and use this new condition to confirm\u0000that the problem is indeed NP-hard. In the second part of the article, we\u0000establish a dichotomy for Boolean PCSPs defined by templates with polymorphisms\u0000in the set of linear threshold functions. The reasoning relies on the new\u0000injective condition.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
You Can't Solve These Super Mario Bros. Levels: Undecidable Mario Games 你解不开的超级马里奥兄弟关卡不可解的马里奥游戏
arXiv - CS - Computational Complexity Pub Date : 2024-05-17 DOI: arxiv-2405.10546
MIT Hardness Group, Hayashi Ani, Erik D. Demaine, Holden Hall, Ricardo Ruiz, Naveen Venkat
{"title":"You Can't Solve These Super Mario Bros. Levels: Undecidable Mario Games","authors":"MIT Hardness Group, Hayashi Ani, Erik D. Demaine, Holden Hall, Ricardo Ruiz, Naveen Venkat","doi":"arxiv-2405.10546","DOIUrl":"https://doi.org/arxiv-2405.10546","url":null,"abstract":"We prove RE-completeness (and thus undecidability) of several 2D games in the\u0000Super Mario Bros. platform video game series: the New Super Mario Bros. series\u0000(original, Wii, U, and 2), and both Super Mario Maker games in all five game\u0000styles (Super Mario Bros. 1 and 3, Super Mario World, New Super Mario Bros. U,\u0000and Super Mario 3D World). These results hold even when we restrict to\u0000constant-size levels and screens, but they do require generalizing to allow\u0000arbitrarily many enemies at each location and onscreen, as well as allowing for\u0000exponentially large (or no) timer. Our New Super Mario Bros. constructions fit\u0000within one standard screen size. In our Super Mario Maker reductions, we work\u0000within the standard screen size and use the property that the game engine\u0000remembers offscreen objects that are global because they are supported by\u0000\"global ground\". To prove these Mario results, we build a new theory of counter\u0000gadgets in the motion-planning-through-gadgets framework, and provide a suite\u0000of simple gadgets for which reachability is RE-complete.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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