108 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Parallel and Flow-Based High Quality Hypergraph Partitioning

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    Balanced hypergraph partitioning is a classic NP-hard optimization problem that is a fundamental tool in such diverse disciplines as VLSI circuit design, route planning, sharding distributed databases, optimizing communication volume in parallel computing, and accelerating the simulation of quantum circuits. Given a hypergraph and an integer kk, the task is to divide the vertices into kk disjoint blocks with bounded size, while minimizing an objective function on the hyperedges that span multiple blocks. In this dissertation we consider the most commonly used objective, the connectivity metric, where we aim to minimize the number of different blocks connected by each hyperedge. The most successful heuristic for balanced partitioning is the multilevel approach, which consists of three phases. In the coarsening phase, vertex clusters are contracted to obtain a sequence of structurally similar but successively smaller hypergraphs. Once sufficiently small, an initial partition is computed. Lastly, the contractions are successively undone in reverse order, and an iterative improvement algorithm is employed to refine the projected partition on each level. An important aspect in designing practical heuristics for optimization problems is the trade-off between solution quality and running time. The appropriate trade-off depends on the specific application, the size of the data sets, and the computational resources available to solve the problem. Existing algorithms are either slow, sequential and offer high solution quality, or are simple, fast, easy to parallelize, and offer low quality. While this trade-off cannot be avoided entirely, our goal is to close the gaps as much as possible. We achieve this by improving the state of the art in all non-trivial areas of the trade-off landscape with only a few techniques, but employed in two different ways. Furthermore, most research on parallelization has focused on distributed memory, which neglects the greater flexibility of shared-memory algorithms and the wide availability of commodity multi-core machines. In this thesis, we therefore design and revisit fundamental techniques for each phase of the multilevel approach, and develop highly efficient shared-memory parallel implementations thereof. We consider two iterative improvement algorithms, one based on the Fiduccia-Mattheyses (FM) heuristic, and one based on label propagation. For these, we propose a variety of techniques to improve the accuracy of gains when moving vertices in parallel, as well as low-level algorithmic improvements. For coarsening, we present a parallel variant of greedy agglomerative clustering with a novel method to resolve cluster join conflicts on-the-fly. Combined with a preprocessing phase for coarsening based on community detection, a portfolio of from-scratch partitioning algorithms, as well as recursive partitioning with work-stealing, we obtain our first parallel multilevel framework. It is the fastest partitioner known, and achieves medium-high quality, beating all parallel partitioners, and is close to the highest quality sequential partitioner. Our second contribution is a parallelization of an n-level approach, where only one vertex is contracted and uncontracted on each level. This extreme approach aims at high solution quality via very fine-grained, localized refinement, but seems inherently sequential. We devise an asynchronous n-level coarsening scheme based on a hierarchical decomposition of the contractions, as well as a batch-synchronous uncoarsening, and later fully asynchronous uncoarsening. In addition, we adapt our refinement algorithms, and also use the preprocessing and portfolio. This scheme is highly scalable, and achieves the same quality as the highest quality sequential partitioner (which is based on the same components), but is of course slower than our first framework due to fine-grained uncoarsening. The last ingredient for high quality is an iterative improvement algorithm based on maximum flows. In the sequential setting, we first improve an existing idea by solving incremental maximum flow problems, which leads to smaller cuts and is faster due to engineering efforts. Subsequently, we parallelize the maximum flow algorithm and schedule refinements in parallel. Beyond the strive for highest quality, we present a deterministically parallel partitioning framework. We develop deterministic versions of the preprocessing, coarsening, and label propagation refinement. Experimentally, we demonstrate that the penalties for determinism in terms of partition quality and running time are very small. All of our claims are validated through extensive experiments, comparing our algorithms with state-of-the-art solvers on large and diverse benchmark sets. To foster further research, we make our contributions available in our open-source framework Mt-KaHyPar. While it seems inevitable, that with ever increasing problem sizes, we must transition to distributed memory algorithms, the study of shared-memory techniques is not in vain. With the multilevel approach, even the inherently slow techniques have a role to play in fast systems, as they can be employed to boost quality on coarse levels at little expense. Similarly, techniques for shared-memory parallelism are important, both as soon as a coarse graph fits into memory, and as local building blocks in the distributed algorithm

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    A decision support system for integrated semi-centralised urban wastewater treatment systems

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    The importance of adequate water supply and sanitation infrastructure as cornerstones for the development of civilizations is undeniable. Although a strategy based on centralised infrastructure has proven to be successful in the past, in some circumstances such conventional systems are inappropriate for future needs. A Semi-centralised Urban Wastewater Treatment System (SUWWTS) may be considered a viable sustainable urban water management solution to promote water security. A SUWWTS merges regulations of traditional centralised systems with the concepts of close-loop and resource recovery of decentralised systems. However, research on the design and feasibility of implementing semi-centralised systems is in its infancy. This Thesis is a first attempt to articulate the complexity, to systematize and to automatize the design of a SUWWTS. Here we show a novel method, referred to as framework, for the development of SUWWTS with allowance for the socio-economic and geographic context of any urban area. To demonstrate the proposed framework a Decision Support System (DSS) was developed; its output is a recommended design comprised of several wastewater treatment plants, their respective technology, and their associated sewerage and reclaimed water distribution networks. The results demonstrate the capabilities and the usefulness of the DSS; it applies the design engineers’ subjective preferences, such as regional technological inclinations and implementation strategies. The results from a feasibility study on the city of Rio de Janeiro validated and demonstrated how the DSS can be used to assist decision-makers. This Thesis discusses the framework, the DSS and the demonstration case. Overall, it will hopefully help both other researchers and practitioners by contributing to the discussion on how to promote urban water security, to decrease urban areas’ dependency on ecosystem services whilst delivering better social welfare

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum

    LIPIcs, Volume 244, ESA 2022, Complete Volume

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    LIPIcs, Volume 244, ESA 2022, Complete Volum

    Super-Cubic Lower Bound for Generalized Karchmer-Wigderson Games

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    In this paper, we prove a super-cubic lower bound on the size of a communication protocol for generalized Karchmer-Wigderson game for an explicit function f: {0,1}? ? {0,1}^{log n}. Lower bounds for original Karchmer-Wigderson games correspond to De Morgan formula lower bounds, thus the best known size lower bound is cubic. The generalized Karchmer-Wigderson games are similar to the original ones, so we hope that our approach can provide an insight for proving better lower bounds on the original Karchmer-Wigderson games, and hence for proving new lower bounds on De Morgan formula size. To achieve super-cubic lower bound we adapt several techniques used in formula complexity to communication protocols, prove communication complexity lower bound for a composition of several functions with a multiplexer relation, and use a technique from [Ivan Mihajlin and Alexander Smal, 2021] to extract the "hardest" function from it. As a result, in this setting we are able to show that there is a relatively small set of functions such that at least one of them does not have a small protocol. The resulting lower bound of ??(n^3.156) is significantly better than the bound obtained from the counting argument

    Oblivious Transfer from Trapdoor Permutations in Minimal Rounds

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    Oblivious transfer (OT) is a foundational primitive within cryptography owing to its connection with secure computation. One of the oldest constructions of oblivious transfer was from certified trapdoor permutations (TDPs). However several decades later, we do not know if a similar construction can be obtained from TDPs in general. In this work, we study the problem of constructing round optimal oblivious transfer from trapdoor permutations. In particular, we obtain the following new results (in the plain model) relying on TDPs in a black-box manner: 1) Three-round oblivious transfer protocol that guarantees indistinguishability-security against malicious senders (and semi-honest receivers). 2) Four-round oblivious transfer protocol secure against malicious adversaries with black-box simulation-based security. By combining our second result with an already known compiler we obtain the first round-optimal 2-party computation protocol that relies in a black-box way on TDPs. A key technical tool underlying our results is a new primitive we call dual witness encryption (DWE) that may be of independent interest

    Abstract Dependency Graphs for Model Verification

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