167 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    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

    Indigenous Territorial Autonomy and Self-Government in the Diverse Americas

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    Across the Americas, Indigenous and Afro-descendent peoples have demanded autonomy, self-determination, and self-governance. By exerting their collective rights, they have engaged with domestic and international standards on the rights of Indigenous Peoples, implemented full-fledged mechanisms for autonomous governance, and promoted political and constitutional reform aimed at expanding understandings of multicultural citizenship and the plurinational state. Yet these achievements come in conflict with national governments’ adoption of neoliberal economic and neo-extractive policies which advance their interests over those of Indigenous communities. Available for the first time in English, Indigenous Territorial Autonomy and Self-Government in the Diverse Americas explores current and historical struggles for autonomy within ancestral territories, experiences of self-governance in operation, and presents an overview of achievements, challenges, and threats across three decades. Case studies across Bolivia, Chile, Nicaragua, Peru, Colombia, Mexico, Panama, Ecuador, and Canada provide a detailed discussion of autonomy and self-governance in development and in practice. Paying special attention to the role of Indigenous peoples’ organizations and activism in pursuing sociopolitical transformation, securing rights, and confronting multiple dynamics of dispossession, this book engages with current debates on Indigenous politics, relationships with national governments and economies, and the multicultural and plurinational state. This book will spark critical reflection on political experience and further exploration of the possibilities of the self-determination of peoples through territorial autonomies

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Efficient Algorithms and Hardness Results for the Weighted k-Server Problem

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    Sub-Exponential Lower Bounds for Branch-and-Bound with General Disjunctions via Interpolation

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    This paper investigates linear programming based branch-and-bound using general disjunctions, also known as stabbing planes, for solving integer programs. We derive the first sub-exponential lower bound (in the encoding length LL of the integer program) for the size of a general branch-and-bound tree for a particular class of (compact) integer programs, namely 2Ω(L1/12ϵ)2^{\Omega(L^{1/12 -\epsilon})} for every ϵ>0\epsilon >0. This is achieved by showing that general branch-and-bound admits quasi-feasible monotone real interpolation, which allows us to utilize sub-exponential lower-bounds for monotone real circuits separating the so-called clique-coloring pair. One important ingredient of the proof is that for every general branch-and-bound tree proving integer-freeness of a product P×QP\times Q of two polytopes PP and QQ, there exists a closely related branch-and-bound tree for showing integer-freeness of PP or one showing integer-freeness of QQ. Moreover, we prove that monotone real circuits can perform binary search efficiently

    Efficient Algorithms and Hardness Results for the Weighted kk-Server Problem

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    In this paper, we study the weighted kk-server problem on the uniform metric in both the offline and online settings. We start with the offline setting. In contrast to the (unweighted) kk-server problem which has a polynomial-time solution using min-cost flows, there are strong computational lower bounds for the weighted kk-server problem, even on the uniform metric. Specifically, we show that assuming the unique games conjecture, there are no polynomial-time algorithms with a sub-polynomial approximation factor, even if we use cc-resource augmentation for c<2c < 2. Furthermore, if we consider the natural LP relaxation of the problem, then obtaining a bounded integrality gap requires us to use at least \ell resource augmentation, where \ell is the number of distinct server weights. We complement these results by obtaining a constant-approximation algorithm via LP rounding, with a resource augmentation of (2+ϵ)(2+\epsilon)\ell for any constant ϵ>0\epsilon > 0. In the online setting, an exp(k)\exp(k) lower bound is known for the competitive ratio of any randomized algorithm for the weighted kk-server problem on the uniform metric. In contrast, we show that 22\ell-resource augmentation can bring the competitive ratio down by an exponential factor to only O(2log)O(\ell^2 \log \ell). Our online algorithm uses the two-stage approach of first obtaining a fractional solution using the online primal-dual framework, and then rounding it online.Comment: This paper will appear in the proceedings of APPROX 202

    On the integration of Dantzig-Wolfe and Fenchel decompositions via directional normalizations

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    The strengthening of linear relaxations and bounds of mixed integer linear programs has been an active research topic for decades. Enumeration-based methods for integer programming like linear programming-based branch-and-bound exploit strong dual bounds to fathom unpromising regions of the feasible space. In this paper, we consider the strengthening of linear programs via a composite of Dantzig-Wolfe and Fenchel decompositions. We provide geometric interpretations of these two classical methods. Motivated by these geometric interpretations, we introduce a novel approach for solving Fenchel sub-problems and introduce a novel decomposition combining Dantzig-Wolfe and Fenchel decompositions in an original manner. We carry out an extensive computational campaign assessing the performance of the novel decomposition on the unsplittable flow problem. Very promising results are obtained when the new approach is compared to classical decomposition methods

    Online Dynamic Acknowledgement with Learned Predictions

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    We revisit the online dynamic acknowledgment problem. In the problem, a sequence of requests arrive over time to be acknowledged, and all outstanding requests can be satisfied simultaneously by one acknowledgement. The goal of the problem is to minimize the total request delay plus acknowledgement cost. This elegant model studies the trade-off between acknowledgement cost and waiting experienced by requests. The problem has been well studied and the tight competitive ratios have been determined. For this well-studied problem, we focus on how to effectively use machine-learned predictions to have better performance. We develop algorithms that perform arbitrarily close to the optimum with accurate predictions while concurrently having the guarantees arbitrarily close to what the best online algorithms can offer without access to predictions, thereby achieving simultaneous optimum consistency and robustness. This new result is enabled by our novel prediction error measure. No error measure was defined for the problem prior to our work, and natural measures failed due to the challenge that requests with different arrival times have different effects on the objective. We hope our ideas can be used for other online problems with temporal aspects that have been resisting proper error measures.Comment: To appear in INFOCOM 202

    Middle-mile optimization for next-day delivery

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    We consider an e-commerce retailer operating a supply chain that consists of middle- and last-mile transportation, and study its ability to deliver products stored in warehouses within a day from customer's order time. Successful next-day delivery requires inventory availability and timely truck schedules in the middle-mile and in this paper we assume a fixed inventory position and focus on optimizing the middle-mile. We formulate a novel optimization problem which decides the departure of the last middle-mile truck at each (potential) network connection in order to maximize the number of next-day deliveries. We show that the respective \emph{next-day delivery optimization} is a combinatorial problem that is NPNP-hard to approximate within (11/e)opt0.632opt(1-1/e)\cdot\texttt{opt}\approx 0.632\cdot\texttt{opt}, hence every retailer that offers one-day deliveries has to deal with this complexity barrier. We study three variants of the problem motivated by operational constraints that different retailers encounter, and propose solutions schemes tailored to each problem's properties. To that end, we rely on greedy submodular maximization, pipage rounding techniques, and Lagrangian heuristics. The algorithms are scalable, offer optimality gap guarantees, and evaluated in realistic datasets and network scenarios were found to achieve near-optimal results
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