292 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Infinitary cut-elimination via finite approximations

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    We investigate non-wellfounded proof systems based on parsimonious logic, a weaker variant of linear logic where the exponential modality ! is interpreted as a constructor for streams over finite data. Logical consistency is maintained at a global level by adapting a standard progressing criterion. We present an infinitary version of cut-elimination based on finite approximations, and we prove that, in presence of the progressing criterion, it returns well-defined non-wellfounded proofs at its limit. Furthermore, we show that cut-elimination preserves the progressive criterion and various regularity conditions internalizing degrees of proof-theoretical uniformity. Finally, we provide a denotational semantics for our systems based on the relational model

    Robust Communication Complexity of Matching: EDCS Achieves 5/6 Approximation

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    Context-Bounded Verification of Context-Free Specifications

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    Independent Sets in Elimination Graphs with a Submodular Objective

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    Maximum weight independent set (MWIS) admits a 1k\frac1k-approximation in inductively kk-independent graphs and a 12k\frac{1}{2k}-approximation in kk-perfectly orientable graphs. These are a a parameterized class of graphs that generalize kk-degenerate graphs, chordal graphs, and intersection graphs of various geometric shapes such as intervals, pseudo-disks, and several others. We consider a generalization of MWIS to a submodular objective. Given a graph G=(V,E)G=(V,E) and a non-negative submodular function f:2VR+f: 2^V \rightarrow \mathbb{R}_+, the goal is to approximately solve maxSIGf(S)\max_{S \in \mathcal{I}_G} f(S) where IG\mathcal{I}_G is the set of independent sets of GG. We obtain an Ω(1k)\Omega(\frac1k)-approximation for this problem in the two mentioned graph classes. The first approach is via the multilinear relaxation framework and a simple contention resolution scheme, and this results in a randomized algorithm with approximation ratio at least 1e(k+1)\frac{1}{e(k+1)}. This approach also yields parallel (or low-adaptivity) approximations. Motivated by the goal of designing efficient and deterministic algorithms, we describe two other algorithms for inductively kk-independent graphs that are inspired by work on streaming algorithms: a preemptive greedy algorithm and a primal-dual algorithm. In addition to being simpler and faster, these algorithms, in the monotone submodular case, yield the first deterministic constant factor approximations for various special cases that have been previously considered such as intersection graphs of intervals, disks and pseudo-disks.Comment: Extended abstract to appear in Proceedings of APPROX 2023. v2 corrects technical typos in few place

    On the Succinctness of Good-for-MDPs Automata

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    Good-for-MDPs and good-for-games automata are two recent classes of nondeterministic automata that reside between general nondeterministic and deterministic automata. Deterministic automata are good-for-games, and good-for-games automata are good-for-MDPs, but not vice versa. One of the question this raises is how these classes relate in terms of succinctness. Good-for-games automata are known to be exponentially more succinct than deterministic automata, but the gap between good-for-MDPs and good-for-games automata as well as the gap between ordinary nondeterministic automata and those that are good-for-MDPs have been open. We establish that these gaps are exponential, and sharpen this result by showing that the latter gap remains exponential when restricting the nondeterministic automata to separating safety or unambiguous reachability automata.Comment: 18 page

    The Worst-Case Complexity of Symmetric Strategy Improvement

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    Symmetric strategy improvement is an algorithm introduced by Schewe et al. (ICALP 2015) that can be used to solve two-player games on directed graphs such as parity games and mean payoff games. In contrast to the usual well-known strategy improvement algorithm, it iterates over strategies of both players simultaneously. The symmetric version solves the known worst-case examples for strategy improvement quickly, however its worst-case complexity remained open. We present a class of worst-case examples for symmetric strategy improvement on which this symmetric version also takes exponentially many steps. Remarkably, our examples exhibit this behaviour for any choice of improvement rule, which is in contrast to classical strategy improvement where hard instances are usually hand-crafted for a specific improvement rule. We present a generalized version of symmetric strategy iteration depending less rigidly on the interplay of the strategies of both players. However, it turns out it has the same shortcomings

    Stronger 3-SUM Lower Bounds for Approximate Distance Oracles via Additive Combinatorics

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    The "short cycle removal" technique was recently introduced by Abboud, Bringmann, Khoury and Zamir (STOC '22) to prove fine-grained hardness of approximation. Its main technical result is that listing all triangles in an n1/2n^{1/2}-regular graph is n2o(1)n^{2-o(1)}-hard under the 3-SUM conjecture even when the number of short cycles is small; namely, when the number of kk-cycles is O(nk/2+γ)O(n^{k/2+\gamma}) for γ<1/2\gamma<1/2. Abboud et al. achieve γ1/4\gamma\geq 1/4 by applying structure vs. randomness arguments on graphs. In this paper, we take a step back and apply conceptually similar arguments on the numbers of the 3-SUM problem. Consequently, we achieve the best possible γ=0\gamma=0 and the following lower bounds under the 3-SUM conjecture: * Approximate distance oracles: The seminal Thorup-Zwick distance oracles achieve stretch 2k±O(1)2k\pm O(1) after preprocessing a graph in O(mn1/k)O(m n^{1/k}) time. For the same stretch, and assuming the query time is no(1)n^{o(1)} Abboud et al. proved an Ω(m1+112.7552k)\Omega(m^{1+\frac{1}{12.7552 \cdot k}}) lower bound on the preprocessing time; we improve it to Ω(m1+12k)\Omega(m^{1+\frac1{2k}}) which is only a factor 2 away from the upper bound. We also obtain tight bounds for stretch 2+o(1)2+o(1) and 3ϵ3-\epsilon and higher lower bounds for dynamic shortest paths. * Listing 4-cycles: Abboud et al. proved the first super-linear lower bound for listing all 4-cycles in a graph, ruling out (m1.1927+t)1+o(1)(m^{1.1927}+t)^{1+o(1)} time algorithms where tt is the number of 4-cycles. We settle the complexity of this basic problem by showing that the O~(min(m4/3,n2)+t)\widetilde{O}(\min(m^{4/3},n^2) +t) upper bound is tight up to no(1)n^{o(1)} factors. Our results exploit a rich tool set from additive combinatorics, most notably the Balog-Szemer\'edi-Gowers theorem and Rusza's covering lemma. A key ingredient that may be of independent interest is a subquadratic algorithm for 3-SUM if one of the sets has small doubling.Comment: Abstract shortened to fit arXiv requirement

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Asymptotically Tight Bounds on the Time Complexity of Broadcast and Its Variants in Dynamic Networks

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