A PTAS for Bounded-Capacity Vehicle Routing in Planar Graphs

The Capacitated Vehicle Routing problem is to find a minimum-cost set of tours that collectively cover clients in a graph, such that each tour starts and ends at a specified depot and is subject to a capacity bound on the number of clients it can serve. In this paper, we present a polynomial-time approximation scheme (PTAS) for instances in which the input graph is planar and the capacity is bounded. Previously, only a quasipolynomial-time approximation scheme was known for these instances. To obtain this result, we show how to embed planar graphs into bounded-treewidth graphs while preserving, in expectation, the client-to-client distances up to a small additive error proportional to client distances to the depot

ON PARAMETERIZED COMPLEXITY OF HITTING SET PROBLEM FOR AXIS–PARALLEL SQUARES INTERSECTING A STRAIGHT LINE

The Hitting Set Problem (HSP) is the well known extremal problem adopting research interest in the fields of combinatorial optimization, computational geometry, and statistical learning theory for decades. In the general setting, the problem is NP-hard and hardly approximable. Also, the HSP remains intractable even in very specific geometric settings, e.g. for axis-parallel rectangles intersecting a given straight line. Recently, for the special case of the problem, where all the rectangles are unit squares, a polynomial but very time consuming optimal algorithm was proposed. We improve this algorithm to decrease its complexity bound more than 100 degrees of magnitude. Also, we extend it to the more general case of the problem  and show that the geometric HSP for axis-parallel (not necessarily unit) squares intersected by a line is polynomially solvable for any fixed range of squares to hit

Linear time algorithm for Precedence Constrained Asymmetric Generalized Traveling Salesman Problem

We consider the combinatorial optimization problem of visiting clusters of a fixed number of nodes (cities), where, on the set of clusters should be visited according to some kind of partial order defined by additional precedence constraints. This problem is a kind of the Asymmetric Generalized Traveling Salesman Problem (AGTSP). To find an optimal solution of the problem, we propose a dynamic programming based on algorithm extending the well known Held and Karp technique. In terms of special type of precedence constraints, we describe subclasses of the problem, with polynomial (or even linear) in n upper bounds of time complexity. © 2016Russian Science Foundation, RSF: 14-11-00109This research was supported by the Russian Science Foundation, grant No. 14-11-00109

Towards an efficient approximability for the Euclidean capacitated vehicle routing problem with time windows and multiple depots

We consider the Euclidean Capacitated Vehicle Routing Problem with Time Windows (CVRPTW). For the long time, approximability of this well-known problem in the class of algorithms with theoretical guarantees was poorly studied. This year, for the case of a single depot, we proposed two approximation algorithms, which are the Efficient Polynomial Time Approximation Schemes (EPTAS) for any fixed given capacity q and the number p of mutually disjunctive time windows. The former scheme extends the celebrated approach proposed by M. Haimovich and A. Rinnooy Kan and allows the evident parallelization, while the latter one has an improved time complexity bound and the enlarged domain in terms q = q(n) and p = p(n), where it retains polynomial time complexity. In this paper, we announce an extension of these results to the case of multiple depots. So, the first scheme is also EPTAS for any fixed parameters q, p, and m, where m is the number of depots, and remains PTAS for q = o(log log n) and mp = o(log log n). In other turn, the second one is a PTAS for p3q4 = O(log n) and (pq)2 log m = O(log n). © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.Russian Foundation for Basic Research, RFBR: 17-08-01385, 19-07-01243Michaeffi Khachay was supported by the Russian Foundation for Basic Research, grants no. 17-08-01385 and 19-07-01243

Polynomial Time Approximation Scheme for the Minimum-weight k-Size Cycle Cover Problem in Euclidean space of an arbitrary fixed dimension

We study the Min-k-SCCP on the partition of a complete weighted digraph by k vertex-disjoint cycles of minimum total weight. This problem is the generalization of the well-known traveling salesman problem (TSP) and the special case of the classical vehicle routing problem (VRP). It is known that the problem Min-k-SCCP is strongly NP-hard and remains intractable even in the geometric statement. For the Euclidean Min-k-SCCP in Rd, we construct a polynomial-time approximation scheme, which generalizes the approach proposed earlier for the planar Min-2-SCCP. For any fixed c > 1, the scheme finds a (1 + 1/c)-approximate solution in time of O(nd+1(k log n)(O (√dc))d-1 2k). © 201

How to Increase the Accuracy of Crowdsourcing Campaigns?

Crowdsourcing is a new approach to performing tasks, with a group of volunteers rather than experts. For example, the Geo-Wiki project [1] aims to improve the global land-cover map by crowdsourcing for image recognition. Though crowdsourcing gives a simple way to perform tasks that are hard to automate, analysis of data received from non-experts is a challenging problem that requires a holistic approach. Here we study in detail the dataset of the Cropland Capture game (part of Geo-Wiki project) to increase the accuracy of campaign’s results. Using this analysis, we developed a methodology for a generic type of crowdsourcing campaign similar to the Cropland Capture game. The proposed methodology relies on computer vision and machine learning techniques. Using the Cropland Capture dataset we showed that our methodology increases agreement between aggregated volunteers’ votes and experts’ decisions from 77% to 86%. [1] Fritz, Steffen, et al. “Geo-Wiki. Org: The use of crowdsourcing to improve global land cover.” Remote Sensing 1.3 (2009): 345-354

Improved Vote Aggregation Techniques for the Geo-Wiki Cropland Capture Crowdsourcing Game

Crowdsourcing is a new approach for solving data processing problems for which conventional methods appear to be inaccurate, expensive, or time-consuming. Nowadays, the development of new crowdsourcing techniques is mostly motivated by so called Big Data problems, including problems of assessment and clustering for large datasets obtained in aerospace imaging, remote sensing, and even in social network analysis. By involving volunteers from all over the world, the Geo-Wiki project tackles problems of environmental monitoring with applications to flood resilience, biomass data analysis and classification of land cover. For example, the Cropland Capture Game, which is a gamified version of Geo-Wiki, was developed to aid in the mapping of cultivated land, and was used to gather 4.5 million image classifications from the Earth’s surface. More recently, the Picture Pile game, which is a more generalized version of Cropland Capture, aims to identify tree loss over time from pairs of very high resolution satellite images. Despite recent progress in image analysis, the solution to these problems is hard to automate since human experts still outperform the majority of machine learning algorithms and artificial systems in this field on certain image recognition tasks. The replacement of rare and expensive experts by a team of distributed volunteers seems to be promising, but this approach leads to challenging questions such as: how can individual opinions be aggregated optimally, how can confidence bounds be obtained, and how can the unreliability of volunteers be dealt with? In this paper, on the basis of several known machine learning techniques, we propose a technical approach to improve the overall performance of the majority voting decision rule used in the Cropland Capture Game. The proposed approach increases the estimated consistency with expert opinion from 77% to 86%

New Geophysical Electromagnetic Method of Archeological Object Research in Egypt

The demand to the enhanced geophysical technique and device, in addition to the precise interpretation of the geophysical data, is the resolution of the geophysical complex research, especially by the absence of priory information about the researched place. Therefore, an approach to use the planshet method of electromagnetic induction in the frequency geometry was developed by Hachay. et al., 1997a, 1997b, 1999, 2000, 2002, and 2005. The method was adapted to map and monitor the high complicated geological mediums, to determine the structural factors and criteria of the rock massif in the mine subsurface

Geophysical contribution to evaluate the hydrothermal potentiality in egypt: case study: hammam faraun and abu swiera, sinai, egypt

The geothermal potentiality in Egypt has a minor significance in the aspects of the Egyptians life, while the hydraulic and hydrocarbonresources are more convenient. However, some other applications for the geothermal activity such as direct warming, pools, and physiotherapy make the research for geothermal as requested. In the present work, two locations with rather good geothermal potentiality will be studied; these are HammamFaraun and Abu Swiera (water temperature is about 70 °C; at Sinai Peninsula).The contribution of the geophysical techniques to evaluate such potentiality could be considered, as its capability to identifythe reservoir characteristics and its implementation is acceptable. Therefore, a geophysical survey program has been conductedin terms of seventeen vertical electrical soundings (VES) and two wide profiles of Control Source Electromagnetic (CSEM) forward step at HammamFaraun and two wide profiles of CSEM at Abu Swiera. The geophysical techniques yield information on the spatial distribution of electrical conductivity, which is the most sensitive parameter to fluids in the rocks. The analysis of the geophysical data, together with the field and geochemical studies lead to the conclusion that, the thermalwater in the subsurface formations might be considered as the preferred cause of the high conductivity in the subsurface on/close to the boarder of tectonically active regions, particularly, where the anomalous conductivity is correlated with high heat flow and other geophysical and geological parameters