A simple algorithm for finding all k-edge-connected components

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Integration of Structural Constraints into TSP Models

International audienceSeveral models based on constraint programming have been proposed to solve the traveling salesman problem (TSP). The most efficient ones, such as the weighted circuit constraint (WCC), mainly rely on the Lagrangian relaxation of the TSP, based on the search for spanning tree or more precisely "1-tree". The weakness of these approaches is that they do not include enough structural constraints and are based almost exclusively on edge costs. The purpose of this paper is to correct this drawback by introducing the Hamiltonian cycle constraint associated with propagators. We propose some properties preventing the existence of a Hamiltonian cycle in a graph or, conversely, properties requiring that certain edges be in the TSP solution set. Notably, we design a propagator based on the research of k-cutsets. The combination of this constraint with the WCC constraint allows us to obtain, for the resolution of the TSP, gains of an order of magnitude for the number of backtracks as well as a strong reduction of the computation time

A general program scheme for finding bridges

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Online uniformly inserting points on grid

LNCS v. 6124 is conference proceedings of 6th international conference, AAIM 2010In this paper, we consider the problem of inserting points in a square grid, which has many background applications, including halftone in reprographic and image processing. We consider an online version of this problem, i.e., the points are inserted one at a time. The objective is to distribute the points as uniformly as possible. Precisely speaking, after each insertion, the gap ratio should be as small as possible. In this paper, we give an insertion strategy with a maximal gap ratio no more than 2 √2 ≈ 2.828, which is the first result on uniformly inserting point in a grid. Moreover, we show that no online algorithm can achieve the maximal gap ratio strictly less than 2.5 for a 3 × 3 grid. © Springer-Verlag Berlin Heidelberg 2010.link_to_subscribed_fulltextThe 6th International Conference on Algorithmic Aspects in Information and Management (AAIM 2010), Weihai, China, 19-21 June 2010. In Lecture Notes in Computer Science, 2010, v. 6124, p. 281–29

Uniformly inserting points on square grid

We consider the problem of inserting points in a square grid, which has many motivations, including halftoning in reprography and image processing. The points are inserted one at a time. The objective is to distribute the points as uniformly as possible. More specifically, after each insertion, the gap ratio should be as small as possible. We give an insertion strategy with a maximal gap ratio no more than 22≈2.828, which is the first result in uniformly inserting points in a grid. Moreover, we show that no online algorithm can achieve the maximal gap ratio strictly less than 2.5 for a 3×3 grid. © 2011 Elsevier B.V.link_to_subscribed_fulltex

Online algorithms for 1-space bounded 2-dimensional bin packing and square packing

LNCS v. 7936 entitled: Computing and combinatorics: 19th International Conference, COCOON 2013 ... proceedingsIn this paper, we study 1-space bounded 2-dimensional bin packing and square packing. A sequence of rectangular items (square items) arrive one by one, each item must be packed into a square bin of unit size on its arrival without any information about future items. When packing items, 90-rotation is allowed. 1-space bounded means there is only one active bin. If the active bin cannot accommodate the coming item, it will be closed and a new bin will be opened. The objective is to minimize the total number of bins used for packing all items in the sequence. Our contributions are as follows: For 1-space bounded 2-dimensional bin packing, we propose an online packing strategy with competitive ratio 5.06. A lower bound of 3.17 on the competitive ratio is proven. Moreover, we study 1-space bounded square packing, where each item is a square with side length no more than 1. A 4.3-competitive algorithm is achieved, and a lower bound of 2.94 on the competitive ratio is given. All these bounds surpass the previously best known results. © 2013 Springer-Verlag Berlin Heidelberg.link_to_subscribed_fulltex