http://dl.acm.org/citation.cfm?id=3446425 http://dl.acm.org/citation.cfm?id=3446425 Fri, 31 Dec 2021 00:00:00 GMT 3446425 http://dl.acm.org/citation.cfm?id=3481638
The Lempel-Ziv 78 (LZ78) and Lempel-Ziv-Welch (LZW) text factorizations are popular, not only for bare compression but also for building compressed data structures on top of them. Their regular factor structure makes them computable within space bounded by the compressed output size. In this article, we carry out the first thorough study of low-memory LZ78 and LZW text factorization algorithms, introducing more efficient alternatives to the classical methods, as well as new techniques that can run within less memory space than the necessary to hold the compressed file.]]> Sat, 30 Oct 2021 00:00:00 GMT 3481638 http://dl.acm.org/citation.cfm?id=3467968
We experimentally evaluate the practical state-of-the-art in graph bipartization (Odd Cycle Transversal (OCT)), motivated by the need for good algorithms for embedding problems into near-term quantum computing hardware. We assemble a preprocessing suite of fast input reduction routines from the OCT and Vertex Cover (VC) literature and compare algorithm implementations using Quadratic Unconstrained Binary Optimization problems from the quantum literature. We also generate a corpus of frustrated cluster loop graphs, which have previously been used to benchmark quantum annealing hardware. The diversity of these graphs leads to harder OCT instances than in existing benchmarks. In addition to combinatorial branching algorithms for solving OCT directly, we study various reformulations into other NP-hard problems such as VC and Integer Linear Programming (ILP), enabling the use of solvers such as CPLEX.]]> Fri, 08 Oct 2021 00:00:00 GMT 3467968 http://dl.acm.org/citation.cfm?id=3459080
Many computational problems in modern society account to probabilistic reasoning, statistics, and combinatorics. A variety of these real-world questions can be solved by representing the question in (Boolean) formulas and associating the number of models of the formula directly with the answer to the question. Since there has been an increasing interest in practical problem solving for model counting over the past years, the Model Counting Competition was conceived in fall 2019. The competition aims to foster applications, identify new challenging benchmarks, and promote new solvers and improve established solvers for the model counting problem and versions thereof. We hope that the results can be a good indicator of the current feasibility of model counting and spark many new applications.]]> Fri, 08 Oct 2021 00:00:00 GMT 3459080 http://dl.acm.org/citation.cfm?id=3484730
The time complexity of support vector machines (SVMs) prohibits training on huge datasets with millions of data points. Recently, multilevel approaches to train SVMs have been developed to allow for time-efficient training on huge datasets. While regular SVMs perform the entire training in one—time-consuming—optimization step, multilevel SVMs first build a hierarchy of problems decreasing in size that resemble the original problem and then train an SVM model for each hierarchy level, benefiting from the solved models of previous levels. We present a faster multilevel support vector machine that uses a label propagation algorithm to construct the problem hierarchy. Extensive experiments indicate that our approach is up to orders of magnitude faster than the previous fastest algorithm while having comparable classification quality.]]> Fri, 08 Oct 2021 00:00:00 GMT 3484730 http://dl.acm.org/citation.cfm?id=3440015
To cope with the intractability of answering Conjunctive Queries (CQs) and solving Constraint Satisfaction Problems (CSPs), several notions of hypergraph decompositions have been proposed—giving rise to different notions of width, noticeably, plain, generalized, and fractional hypertree width (hw, ghw, and fhw). Given the increasing interest in using such decomposition methods in practice, a publicly accessible repository of decomposition software, as well as a large set of benchmarks, and a web-accessible workbench for inserting, analyzing, and retrieving hypergraphs are called for. We address this need by providing (i) concrete implementations of hypergraph decompositions (including new practical algorithms), (ii) a new, comprehensive benchmark of hypergraphs stemming from disparate CQ and CSP collections, and (iii) HyperBench, our new web-interface for accessing the benchmark and the results of our analyses.]]> Fri, 09 Jul 2021 00:00:00 GMT 3440015 http://dl.acm.org/citation.cfm?id=3450703
Networks model a variety of complex phenomena across different domains. In many applications, one of the most essential tasks is to align two or more networks to infer the similarities between cross-network vertices and to discover potential node-level correspondence. In this article, we propose ELRUNA (elimination rule-based network alignment), a novel network alignment algorithm that relies exclusively on the underlying graph structure. Under the guidance of the elimination rules that we defined, ELRUNA computes the similarity between a pair of cross-network vertices iteratively by accumulating the similarities between their selected neighbors. The resulting cross-network similarity matrix is then used to infer a permutation matrix that encodes the final alignment of cross-network vertices.]]> Fri, 09 Jul 2021 00:00:00 GMT 3450703 http://dl.acm.org/citation.cfm?id=3457197
We present new sequential and parallel algorithms for wavelet tree construction based on a new bottom-up technique. This technique makes use of the structure of the wavelet trees—refining the characters represented in a node of the tree with increasing depth—in an opposite way, by first computing the leaves (most refined), and then propagating this information upwards to the root of the tree. We first describe new sequential algorithms, both in RAM and external memory. Based on these results, we adapt these algorithms to parallel computers, where we address both shared memory and distributed memory settings. In practice, all our algorithms outperform previous ones in both time and memory efficiency, because we can compute all auxiliary information solely based on the information we obtained from computing the leaves.]]> Fri, 09 Jul 2021 00:00:00 GMT 3457197 http://dl.acm.org/citation.cfm?id=3459606
Quantum annealing is getting increasing attention in combinatorial optimization. The quantum processing unit by D-Wave is constructed to approximately solve Ising models on so-called Chimera graphs. Ising models are equivalent to quadratic unconstrained binary optimization (QUBO) problems and maximum cut problems on the associated graphs. We have tailored branch-and-cut as well as semidefinite programming algorithms for solving Ising models for Chimera graphs to provable optimality and use the strength of these approaches for comparing our solution values to those obtained on the current quantum annealing machine, D-Wave 2000Q. This allows for the assessment of the quality of solutions produced by the D-Wave hardware.]]> Fri, 09 Jul 2021 00:00:00 GMT 3459606 http://dl.acm.org/citation.cfm?id=3461698
We introduce the notion of reverse-safe data structures. These are data structures that prevent the reconstruction of the data they encode (i.e., they cannot be easily reversed). A data structure D is called z-reverse-safe when there exist at least z datasets with the same set of answers as the ones stored by D. The main challenge is to ensure that D stores as many answers to useful queries as possible, is constructed efficiently, and has size close to the size of the original dataset it encodes. Given a text of length n and an integer z, we propose an algorithm that constructs a z-reverse-safe data structure (z-RSDS) that has size O(n) and answers decision and counting pattern matching queries of length at most d optimally, where d is maximal for any such z-RSDS.]]> Fri, 09 Jul 2021 00:00:00 GMT 3461698 http://dl.acm.org/citation.cfm?id=3462208
We consider the Windows Scheduling (WS) problem, which is a restricted version of Unit-Fractions Bin Packing, and it is also called Inventory Replenishment in the context of Supply Chain. In brief, WS problem is to schedule the use of communication channels to clients. Each client ci is characterized by an active cycle and a window wi. During the period of time that any given client ci is active, there must be at least one transmission from ci scheduled in any wi consecutive time slots, but at most one transmission can be carried out in each channel per time slot. The goal is to minimize the number of channels used.]]> Fri, 09 Jul 2021 00:00:00 GMT 3462208 http://dl.acm.org/citation.cfm?id=3433651
We consider the problem of computing the triplet distance between two rooted unordered trees with n labeled leaves. Introduced by Dobson in 1975, the triplet distance is the number of leaf triples that induce different topologies in the two trees. The current theoretically fastest algorithm is an O(n log n) algorithm by Brodal et al. (SODA 2013). Recently, Jansson and Rajaby proposed a new algorithm that, while slower in theory, requiring O(n log 3 n) time, in practice it outperforms the theoretically faster O(n log n) algorithm. Both algorithms do not scale to external memory. We present two cache oblivious algorithms that combine the best of both worlds.]]> Sat, 08 May 2021 00:00:00 GMT 3433651 http://dl.acm.org/citation.cfm?id=3439801
Finding a maximum-cardinality or maximum-weight matching in (edge-weighted) undirected graphs is among the most prominent problems of algorithmic graph theory. For n-vertex and m-edge graphs, the best-known algorithms run in Õ(m√ n) time. We build on recent theoretical work focusing on linear-time data reduction rules for finding maximum-cardinality matchings and complement the theoretical results by presenting and analyzing (thereby employing the kernelization methodology of parameterized complexity analysis) new (near-)linear-time data reduction rules for both the unweighted and the positive-integer-weighted case.]]> Fri, 23 Apr 2021 00:00:00 GMT 3439801 http://dl.acm.org/citation.cfm?id=3446429
A feedback arc set of a directed graph G is a subset of its arcs containing at least one arc of every cycle in G. Finding a feedback arc set of minimum cardinality is an NP-hard problem called the minimum feedback arc set problem. Numerically, the minimum set cover formulation of the minimum feedback arc set problem is appropriate as long as all simple cycles in G can be enumerated. Unfortunately, even those sparse graphs that are important for practical applications often have Ω (2n) simple cycles. Here we address precisely such situations: An exact method is proposed for sparse graphs that enumerates simple cycles in a lazy fashion and iteratively extends an incomplete cycle matrix.]]> Fri, 23 Apr 2021 00:00:00 GMT 3446429 http://dl.acm.org/citation.cfm?id=3447652
The classical NP–hard feedback arc set problem (FASP) and feedback vertex set problem (FVSP) ask for a minimum set of arcs ϵ ⊆ E or vertices ν ⊆ V whose removal G ∖ ϵ, G ∖ ν makes a given multi–digraph G=(V, E) acyclic, respectively. Though both problems are known to be APX–hard, constant ratio approximations or proofs of inapproximability are unknown. We propose a new universal O(|V||E|4)–heuristic for the directed FASP. While a ratio of r ≈ 1.3606 is known to be a lower bound for the APX–hardness, at least by empirical validation we achieve an approximation of r ≤ 2.]]> Wed, 31 Mar 2021 00:00:00 GMT 3447652 http://dl.acm.org/citation.cfm?id=3429280
In this article, we consider the problem of identifying patterns of interest in colored strings. A colored string is a string where each position is assigned one of a finite set of colors. Our task is to find substrings of the colored string that always occur followed by the same color at the same distance. The problem is motivated by applications in embedded systems verification, in particular, assertion mining. The goal there is to automatically find properties of the embedded system from the analysis of its simulation traces. We show that, in our setting, the number of patterns of interest is upper-bounded by O(n2), where n is the length of the string.]]> Wed, 30 Dec 2020 00:00:00 GMT 3429280