On approximate data reduction for the Rural Postman Problem: Theory and experiments

Bevern, René van; Fluschnik, Till; Tsidulko, Oxana Yu.

doi:10.1002/net.21985

Cited by 9 publications

(3 citation statements)

References 53 publications

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“…Exact algorithms for NP-complete problems usually take time exponential in the input size. Thus, an important preprocessing step is data reduction, which has proven to quite tremendously shrink real-world instances of NP-hard problems [2,7,8,31]. The main notion of data reduction with performance guarantees is problem kernelization [18], here stated for d-Hitting Set: Definition 2.…”

Section: Introductionmentioning

confidence: 99%

Optimal-size problem kernels for d-Hitting Set in linear time and space

Bevern

Smirnov

2020

Information Processing Letters

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Section: Introductionmentioning

confidence: 99%

Optimal-size problem kernels for d-Hitting Set in linear time and space

Bevern

Smirnov

2020

Information Processing Letters

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“…Exact algorithms for NPcomplete problems usually take time exponential in the input size. Thus, an important preprocessing step is data reduction, which has proven to significantly shrink real-world instances of NP-hard problems [2,3,11,13,14,41,52]. In the context of public transport optimization, Weihe [52] introduced a simple but very effective in experiments [13,14,52] data reduction algorithm for Hitting Set.…”

Section: Problem 11 (Multiple Hitting Set)mentioning

confidence: 99%

Serial and parallel kernelization of Multiple Hitting Set parameterized by the Dilworth number, implemented on the GPU

Bevern¹,

Kirilin²,

Skachkov³

et al. 2021

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The NP-hard Multiple Hitting Set problem is finding a minimum-cardinality set intersecting each of the sets in a given input collection a given number of times. Generalizing a well-known data reduction algorithm due to Weihe, we show a problem kernel for Multiple Hitting Set parameterized by the Dilworth number, a graph parameter introduced by Foldes and Hammer in 1978 yet seemingly so far unexplored in the context of parameterized complexity theory. Using matrix multiplication, we speed up the algorithm to quadratic sequential time and logarithmic parallel time. We experimentally evaluate our algorithms. By implementing our algorithm on GPUs, we show the feasibility of realizing kernelization algorithms on SIMD (Single Instruction, Multiple Date) architectures.

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“…In the framework of lossy kernelization, van Bevern et al [2] study trade‐offs between the provable effect of data reduction and the provably achievable solution quality for a classical arc routing problem: the rural postman problem. Several theoretical results are provided by the authors.…”

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confidence: 99%

Preface: Special issue on arc routing problems and other related topics

2020

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This special issue of Networks is associated with WARP3, the 3rd International Workshop on Arc Routing Problems, which took place in Pizzo (Calabria, Italy) on May 27 to 29, 2019. WARP3 was organized by the Department of Mechanical, Energy and Management Engineering and by the Department of Economics, Statistics and Finance "Giovanni Anania" of the University of Calabria. It followed the first meeting held in Copenhagen in May 2013 and the second meeting held in Lisbon in May 2016, with the aim of bringing together the international community of researchers and practitioners interested in arc routing. Specifically, the workshop provided a high-level forum for scientific exchange and cooperation on models and methods for arc routing problems and strongly related problems. These problems typically arise in logistics and distribution management and, in most cases, are formulated over graphs representing street networks. The event attracted great interest and was attended by people from over 10 countries on different continents. The presentations, which were scheduled in a single stream over 2 days, covered solution methods, complexity issues, and classical and new problems in the broad area of arc routing. However, the related special issue was not restricted to WARP3 talks or attendees. Overall, 13 manuscripts were submitted for publication; of these, 7 were accepted after a rigorous refereeing process and appear in this special issue. The final contents are organized as follows. Fröhlich et al. [5] study a multi-objective periodic mixed capacitated general routing problem, in which nodes, edges, and arcs of the graph must be visited/traversed regularly but with inconsistent routes to ensure the unpredictability of the service patterns. The aim is to find a feasible solution that minimizes the total routing cost while maximizing the route inconsistency. Solving this problem might be interesting for security companies that offer a range of services to protect objects (e.g., cash-in-transit) and people (e.g., patrolling services). The authors obtain an equivalent node-based routing model and design a tailored solution procedure for it. Castro Campos et al. [4] focus on a variant of the windy postman problem. More specifically, they study the plowing with precedence problem in which a plow is required to clean the streets of a town after a heavy snowfall, and travel costs depend on the direction of the traversal, as well as whether a street has been previously plowed or not. The authors prove that the problem can be solved in polynomial time under some natural cost structures. In addition, they propose new and fast heuristics for the problem and compare them with the state-of-the-art. Ahabchane et al. [1] investigate another routing problem arising in the winter season. In particular, their study is motivated by road maintenance when the demand for salt or abrasive on street segments depends on time. The variation of demand is due to the weather or traffic conditions. The authors model the decision problem as a mixed ...

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On approximate data reduction for the Rural Postman Problem: Theory and experiments

Cited by 9 publications

References 53 publications

Optimal-size problem kernels for d-Hitting Set in linear time and space

Optimal-size problem kernels for d-Hitting Set in linear time and space

Serial and parallel kernelization of Multiple Hitting Set parameterized by the Dilworth number, implemented on the GPU

Preface: Special issue on arc routing problems and other related topics

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