Theory of Computing Systems最新文献

{"title":"On Forced Periodicity of Perfect Colorings","authors":"Pyry Herva, J. Kari","doi":"10.1007/s00224-023-10127-x","DOIUrl":"https://doi.org/10.1007/s00224-023-10127-x","url":null,"abstract":"","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46249853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Preface of the Special Issue Dedicated to Selected Papers from CSR 2020","authors":"H. Fernau, M. Volkov","doi":"10.1007/s00224-022-10115-7","DOIUrl":"https://doi.org/10.1007/s00224-022-10115-7","url":null,"abstract":"","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47039049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Preface of STACS 2020 Special Issue","authors":"Christopher Paul, M. Bläser","doi":"10.1007/s00224-022-10116-6","DOIUrl":"https://doi.org/10.1007/s00224-022-10116-6","url":null,"abstract":"","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43225280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"One-Tape Turing Machine and Branching Program Lower Bounds for MCSP","authors":"Mahdi Cheraghchi, Shuichi Hirahara, Dimitrios Myrisiotis, Yuichi Yoshida","doi":"10.1007/s00224-022-10113-9","DOIUrl":"https://doi.org/10.1007/s00224-022-10113-9","url":null,"abstract":"<p>For a size parameter <span>(s:mathbb {N}to mathbb {N})</span>, the Minimum Circuit Size Problem (denoted by MCSP[<i>s</i>(<i>n</i>)]) is the problem of deciding whether the minimum circuit size of a given function <i>f</i> : {0,1}^<i>n</i> →{0,1} (represented by a string of length <i>N</i> := 2^<i>n</i>) is at most a threshold <i>s</i>(<i>n</i>). A recent line of work exhibited “hardness magnification” phenomena for MCSP: A very weak lower bound for MCSP implies a breakthrough result in complexity theory. For example, McKay, Murray, and Williams (STOC 2019) implicitly showed that, for some constant <i>μ</i>₁ &gt; 0, if <span>(text {MCSP}[2^{mu _{1}cdot n}])</span> cannot be computed by a one-tape Turing machine (with an additional one-way read-only input tape) running in time <i>N</i>^1.01, then P≠NP. In this paper, we present the following new lower bounds against one-tape Turing machines and branching programs: (1) A randomized two-sided error one-tape Turing machine (with an additional one-way read-only input tape) cannot compute <span>(text {MCSP}[2^{mu _{2}cdot n}])</span> in time <i>N</i>^1.99, for some constant <i>μ</i>₂ &gt; <i>μ</i>₁. (2) A non-deterministic (or parity) branching program of size <span>(o(N^{1.5}/log N))</span> cannot compute MKTP, which is a time-bounded Kolmogorov complexity analogue of MCSP. This is shown by directly applying the Nečiporuk method to MKTP, which previously appeared to be difficult. (3) The size of any non-deterministic, co-non-deterministic, or parity branching program computing MCSP is at least <span>(N^{1.5-oleft (1right )})</span>. These results are the first non-trivial lower bounds for MCSP and MKTP against one-tape Turing machines and non-deterministic branching programs, and essentially match the best-known lower bounds for any explicit functions against these computational models. The first result is based on recent constructions of pseudorandom generators for read-once oblivious branching programs (ROBPs) and combinatorial rectangles (Forbes and Kelley, FOCS 2018; Viola, Electron. Colloq. Comput. Complexity (ECCC) 26, 51, 2019). En route, we obtain several related results: (1) There exists a (local) hitting set generator with seed length <span>(widetilde {O}(sqrt {N}))</span> secure against read-once polynomial-size non-deterministic branching programs on <i>N</i>-bit inputs. (2) Any read-once co-non-deterministic branching program computing MCSP must have size at least <span>(2^{widetilde {Omega }(N)})</span>.</p>","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138514119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Random Access in Persistent Strings and Segment Selection","authors":"P. Bille, I. L. Gørtz","doi":"10.1007/s00224-022-10109-5","DOIUrl":"https://doi.org/10.1007/s00224-022-10109-5","url":null,"abstract":"","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43025160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A One Pass Streaming Algorithm for Finding Euler Tours","authors":"Christian Glazik, J. Schiemann, A. Srivastav","doi":"10.1007/s00224-022-10077-w","DOIUrl":"https://doi.org/10.1007/s00224-022-10077-w","url":null,"abstract":"","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47944375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Digraph Coloring and Distance to Acyclicity","authors":"Ararat Harutyunyan, Michael Lampis, Nikolaos Melissinos","doi":"10.1007/s00224-022-10103-x","DOIUrl":"https://doi.org/10.1007/s00224-022-10103-x","url":null,"abstract":"<p>In <i>k</i>-<span>Digraph Coloring</span> we are given a digraph and are asked to partition its vertices into at most <i>k</i> sets, so that each set induces a DAG. This well-known problem is NP-hard, as it generalizes (undirected) <i>k</i>-<span>Coloring</span>, but becomes trivial if the input digraph is acyclic. This poses the natural parameterized complexity question of what happens when the input is “almost” acyclic. In this paper we study this question using parameters that measure the input’s distance to acyclicity in either the directed or the undirected sense. In the directed sense perhaps the most natural notion of distance to acyclicity is directed feedback vertex set. It is already known that, for all <i>k</i> ≥ 2, <i>k</i>-<span>Digraph Coloring</span> is NP-hard on digraphs of directed feedback vertex set of size at most <i>k</i> + 4. We strengthen this result to show that, for all <i>k</i> ≥ 2, <i>k</i>-<span>Digraph Coloring</span> is already NP-hard for directed feedback vertex set of size exactly <i>k</i>. This immediately provides a dichotomy, as <i>k</i>-<span>Digraph Coloring</span> is trivial if directed feedback vertex set has size at most <i>k</i> − 1. Refining our reduction we obtain three further consequences: (i) 2-<span>Digraph Coloring</span> is NP-hard for oriented graphs of directed feedback vertex set at most 3; (ii) for all <i>k</i> ≥ 2, <i>k</i>-<span>Digraph Coloring</span> is NP-hard for graphs of feedback <i>arc</i> set of size at most <i>k</i>²; interestingly, this leads to a second dichotomy, as we show that the problem is FPT by <i>k</i> if feedback arc set has size at most <i>k</i>² − 1; (iii) <i>k</i>-<span>Digraph Coloring</span> is NP-hard for graphs of directed feedback vertex <i>k</i>, even if the maximum degree <i>Δ</i> is at most 4<i>k</i> − 1; we show that this is also <i>almost</i> tight, as the problem becomes FPT for digraphs of directed feedback vertex set of size <i>k</i> and <i>Δ</i> ≤ 4<i>k</i> − 3. Since these results imply that the problem is also NP-hard on graphs of bounded directed treewidth, we then consider parameters that measure the distance from acyclicity of the underlying graph. On the positive side, we show that <i>k</i>-<span>Digraph Coloring</span> admits an FPT algorithm parameterized by treewidth, whose parameter dependence is (tw!)<i>k</i>^tw. Since this is considerably worse than the <i>k</i>^tw dependence of (undirected) <i>k</i>-<span>Coloring</span>, we pose the question of whether the tw! factor can be eliminated. Our main contribution in this part is to settle this question in the negative and show that our algorithm is essentially optimal, even for the much more restricted parameter treedepth and for <i>k</i> = 2. Specifically, we show that an FPT algorithm solving 2-<span>Digraph Coloring</span> with dependence td^<i>o</i>(td) would contradict the ETH. Then, we consider the class of tournaments. It is known that","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138514155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Transformation of LL(k)-linear to LL(1)-linear Grammars","authors":"I. Olkhovsky, A. Okhotin","doi":"10.1007/s00224-022-10108-6","DOIUrl":"https://doi.org/10.1007/s00224-022-10108-6","url":null,"abstract":"","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43374939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local Deal-Agreement Algorithms for Load Balancing in Dynamic General Graphs","authors":"Yefim Dinitz, S. Dolev, Manish Kumar","doi":"10.1007/s00224-022-10097-6","DOIUrl":"https://doi.org/10.1007/s00224-022-10097-6","url":null,"abstract":"","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41694025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Correction to: Submodular Functions and Rooted Trees","authors":"Yaokun Wu, Yinfeng Zhu","doi":"10.1007/s00224-022-10099-4","DOIUrl":"https://doi.org/10.1007/s00224-022-10099-4","url":null,"abstract":"","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46494445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}