107 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Geographic information extraction from texts

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    A large volume of unstructured texts, containing valuable geographic information, is available online. This information – provided implicitly or explicitly – is useful not only for scientific studies (e.g., spatial humanities) but also for many practical applications (e.g., geographic information retrieval). Although large progress has been achieved in geographic information extraction from texts, there are still unsolved challenges and issues, ranging from methods, systems, and data, to applications and privacy. Therefore, this workshop will provide a timely opportunity to discuss the recent advances, new ideas, and concepts but also identify research gaps in geographic information extraction

    Tight Bounds on List-Decodable and List-Recoverable Zero-Rate Codes

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    In this work, we consider the list-decodability and list-recoverability of codes in the zero-rate regime. Briefly, a code C[q]n\mathcal{C} \subseteq [q]^n is (p,,L)(p,\ell,L)-list-recoverable if for all tuples of input lists (Y1,,Yn)(Y_1,\dots,Y_n) with each Yi[q]Y_i \subseteq [q] and Yi=|Y_i|=\ell the number of codewords cCc \in \mathcal{C} such that ciYic_i \notin Y_i for at most pnpn choices of i[n]i \in [n] is less than LL; list-decoding is the special case of =1\ell=1. In recent work by Resch, Yuan and Zhang~(ICALP~2023) the zero-rate threshold for list-recovery was determined for all parameters: that is, the work explicitly computes p:=p(q,,L)p_*:=p_*(q,\ell,L) with the property that for all ϵ>0\epsilon>0 (a) there exist infinite families positive-rate (pϵ,,L)(p_*-\epsilon,\ell,L)-list-recoverable codes, and (b) any (p+ϵ,,L)(p_*+\epsilon,\ell,L)-list-recoverable code has rate 00. In fact, in the latter case the code has constant size, independent on nn. However, the constant size in their work is quite large in 1/ϵ1/\epsilon, at least C(1ϵ)O(qL)|\mathcal{C}|\geq (\frac{1}{\epsilon})^{O(q^L)}. Our contribution in this work is to show that for all choices of q,q,\ell and LL with q3q \geq 3, any (p+ϵ,,L)(p_*+\epsilon,\ell,L)-list-recoverable code must have size Oq,,L(1/ϵ)O_{q,\ell,L}(1/\epsilon), and furthermore this upper bound is complemented by a matching lower bound Ωq,,L(1/ϵ)\Omega_{q,\ell,L}(1/\epsilon). This greatly generalizes work by Alon, Bukh and Polyanskiy~(IEEE Trans.\ Inf.\ Theory~2018) which focused only on the case of binary alphabet (and thus necessarily only list-decoding). We remark that we can in fact recover the same result for q=2q=2 and even LL, as obtained by Alon, Bukh and Polyanskiy: we thus strictly generalize their work.Comment: Abstract shortened to meet the arXiv requiremen

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum

    LIPIcs, Volume 258, SoCG 2023, Complete Volume

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    LIPIcs, Volume 258, SoCG 2023, Complete Volum

    Upper density problems in infinite Ramsey theory

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    We consider the following question in infinite Ramsey theory, introduced by Erdős and Galvin [EG93] in a particular case and by DeBiasio and McKenney [DM19] in a more general setting. Let H be a countably infinite graph. If the edges of the complete graph on the natural numbers are colored red or blue, what is the maximum value of λ such that we are guaranteed to find a monochromatic copy of H whose vertex set has upper density at least λ? We call this value the Ramsey density of H. The problem of determining the Ramsey density of the infinite path was first studied by Erdős and Galvin, and was recently solved by Corsten, DeBiasio, Lang and the author [CDLL19]. In this thesis we study the problem of determining the Ramsey density of arbitrary graphs H. On an intuitive level, we show that three properties of a graph H have an effect on the Ramsey density: the chromatic number, the number of components, and the expansion of its independent sets. We deduce the exact value of the Ramsey density for a wide variety of graphs, including all locally finite forests, bipartite factors, clique factors and odd cycle factors. We also determine the value of the Ramsey density of all locally finite graphs, up to a factor of 2. We also study a list coloring variant of the same problem. We show that there exists a way of assigning a list of size two to every edge in the complete graph on N such that, in every list coloring, there are monochromatic paths with density arbitrarily close to 1.Wir betrachten die folgende Fragestellung aus der Ramsey-Theorie, welche von Erdős und Galvin [EG93] in einem Spezialfall sowie von DeBiasio und McKenney [DM19] in einem allgemeineren Kontext formuliert wurde: Es sei H ein abzählbar unendlicher Graph. Welches ist der größtmögliche Wert λ, sodass wir, wenn die Kanten des vollständigen Graphen mit Knotenmenge N jeweils entweder rot oder blau gefärbt sind, stets eine einfarbige Kopie von H, dessen Knotenmenge eine obere asymptotische Dichte von mindestens λ besitzt, finden können? Wir nennen diesen Wert die Ramsey-Dichte von H. Das Problem, die Ramsey-Dichte des unendlichen Pfades zu bestimmen wurde erstmals von Erdős und Galvin untersucht und wurde vor kurzem von Corsten, DeBiasio, Lang und dem Autor [CDLL19] gelöst. Gegenstand der vorliegenden Dissertation ist die Bestimmung der Ramsey-Dichten von Graphen. Auf einer intuitiven Ebene zeigen wir, dass drei Parameter eines Graphen die Ramsey-Dichte beeinflussen: die chromatische Zahl, die Anzahl der Zusammenhangskomponenten sowie die Expansion seiner unabhängigen Mengen. Wir ermitteln die exakten Werte der Ramsey-Dichte für eine Vielzahl von Graphen, darunter alle lokal endlichen Wälder, bipartite Faktoren, Kr-Faktoren sowie Ck-Faktoren für ungerade k. Ferner bestimmen wir den Wert der Ramsey-Dichte aller lokal endlichen Graphen bis auf einen Faktor 2. Darüber hinaus untersuchen wir eine Variante des oben beschriebenen Problems für Listenfärbungen. Wir zeigen, dass es möglich ist, jeder Kante des vollständigen Graphen mit Knotenmenge N eine Liste der Größe Zwei zuzuweisen, sodass in jeder zugehörigen Listenfärbung monochromatische Pfade mit beliebig nah an 1 liegender Dichte existieren

    What is in# P and what is not?

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    For several classical nonnegative integer functions, we investigate if they are members of the counting complexity class #P or not. We prove #P membership in surprising cases, and in other cases we prove non-membership, relying on standard complexity assumptions or on oracle separations. We initiate the study of the polynomial closure properties of #P on affine varieties, i.e., if all problem instances satisfy algebraic constraints. This is directly linked to classical combinatorial proofs of algebraic identities and inequalities. We investigate #TFNP and obtain oracle separations that prove the strict inclusion of #P in all standard syntactic subclasses of #TFNP-1

    LIPIcs, Volume 244, ESA 2022, Complete Volume

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    LIPIcs, Volume 244, ESA 2022, Complete Volum

    Multiclass Learnability Beyond the PAC Framework: Universal Rates and Partial Concept Classes

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    In this paper we study the problem of multiclass classification with a bounded number of different labels kk, in the realizable setting. We extend the traditional PAC model to a) distribution-dependent learning rates, and b) learning rates under data-dependent assumptions. First, we consider the universal learning setting (Bousquet, Hanneke, Moran, van Handel and Yehudayoff, STOC '21), for which we provide a complete characterization of the achievable learning rates that holds for every fixed distribution. In particular, we show the following trichotomy: for any concept class, the optimal learning rate is either exponential, linear or arbitrarily slow. Additionally, we provide complexity measures of the underlying hypothesis class that characterize when these rates occur. Second, we consider the problem of multiclass classification with structured data (such as data lying on a low dimensional manifold or satisfying margin conditions), a setting which is captured by partial concept classes (Alon, Hanneke, Holzman and Moran, FOCS '21). Partial concepts are functions that can be undefined in certain parts of the input space. We extend the traditional PAC learnability of total concept classes to partial concept classes in the multiclass setting and investigate differences between partial and total concepts
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