Showing papers in "Electronic Notes in Discrete Mathematics in 2003"

TL;DR: It is proved that the heuristic asymptotically certainly succeeds in producing a satisfying truth assignment for formulas with clauses to variables ratio (density) of up to 3.52, and not only the satisfiability threshold, but also the threshold where the complexity of searching for satisfying truth assignments jumps from polynomial to exponential is at least3.52.

TL;DR: Bounds on the eigenvalues of a graph G, a simple graph with p vertices and A(G) be the adjacency matrix of G, are given.

TL;DR: An algorithm is developed that reconstructs an L-convex polyomino from the set of its maximal L-polyominoes, a subset of convex polyaminoes whose elements satisfy a special convexity property.

TL;DR: Using Burnside's lemma, it is proved that the number of n-variable rotation symmetric Boolean functions is 2gn, where gn and φ is the Euler phi-function, and there are exactly 8, 48, and 15104, RotS bent functions on 4, 6, and 8 variables respectively.

TL;DR: It is proved that the center of a fuzzy tree consists of either a single node or two nodes joined by a strong arc, and that in a fuzzy Tree, every triple of nodes has a unique median, but not conversely.

TL;DR: In this article, a new concept, fuzzy segments, is introduced which allows for flexible segmentation of discrete curves, so taking into account some noise in them, and a very efficient detection algorithm for fuzzy segments and its application to curve segmentation are presented.

TL;DR: It is shown that the regularized LP-relaxation provides a good approximation and thus allows to bias the reconstruction towards solutions with spatially coherent regions, which provides an alternative to computationally expensive MCMC-sampling (Markov Chain Monte Carlo) techniques and other heuristic rounding schemes.

TL;DR: It is proved that the game chromatic index of forests of maximum node degree 5 is at most 6, which improves the previously known upper bound 7 for this parameter.

TL;DR: It is shown that random 3-SAT formulas with poly(log n) clauses can be efficiently certified as unsatisfiable and improves a previous bound of n3/2 + epsilon clauses.

TL;DR: This article investigates the preimage associated to digital planes and presents structure theorems that describe the pre image of a digital plane and presents a bound on the number of preimage faces.

TL;DR: Comparative experiments with the WalkSAT local search algorithm show behavior somewhat similar to RRT, but with the linear time phase not extending quite as close to the satisfiability threshold.

TL;DR: This work investigates L(h, k)-labelings of trees of maximum degree ∆, seeking those with small span and establishes optimal span of L( h, k-labelings for stars of arbitrary degree and all values of h and k.

TL;DR: The inner-salient and reentrant are defined similarly to the border ones, but it is shown that, in general, they do not characterize the set, even if this set is 4-simply connected.

TL;DR: A convex programming approach to the problem of matching subgraphs which represent object views against larger graphs which represent scenes, extending the linear objective function in order to take into account the relational constraints given by both graphs.

TL;DR: This paper establishes two L-reductions (an approximation preserving reduction) from minimum dominating set problem for fe-regular graphs to minimum monoposyly problem for 2fe- regular graphs and to minimum monopoly problem for (2k -1)-regular graphs, where k ≥ 3.

TL;DR: It is shown that there is such a pattern for the decision problem of MAX-2-SAT associated with the phase transition and that the hardest problems are among those with high allowance for false clauses but low number of clauses.

TL;DR: A new method of description of pictures of digitized rectangular arrays is introduced based on contextual grammars, defined and their properties are studied.

TL;DR: New subsets of symmetric balanced and symmetric correlation immune functions are identified and constructive techniques improve upon the existing lower bounds on the cardinality of the above sets.

TL;DR: The adjacency domination parameters are determined for various semigraphs and a few bounds are obtained.

TL;DR: In this paper, the authors present several ways of improving the time complexity of the original algorithm and give the results of experiments with an optimized version which is much faster than the original implementation, up to a factor of 50 or more.

TL;DR: It is shown that it is not always the case where an edge-clique graph is a clique graph, and it is proved that a minimum counterexample to (* does not hold.

TL;DR: Certain two-weight codes are used to construct secret sharing schemes, and their access structure is analyzed to determine the access structure of these schemes.

TL;DR: This paper proposes a concise coding of the cells of n-dimensional finite regular grids, which induces a simple, generic and efficient framework for implementing classical digital topology data structures and algorithms.

TL;DR: The upper bounds for the tightness threshold for C n,cn 2,k,t to have an exponential resolution complexity are established.

TL;DR: A group divisible design GD (K,M ;υ) is an ordered triple where X is a set with cardinality υ, G is aSet of subsets (called groups) of X such that G partitions X and ∣G∣ ∈ M for each G ∈ G , and B is aset of subset of Xsuch that each pair of distinct elements of X is contained either in a unique group or in aunique block, but not both.

TL;DR: This paper introduces a series of criteria each having a linear-time complexity to progressively solve the min DSS problem, and results in an optimal algorithm both from the point of view of optimization and of complexity, outperforming the previous quadratic bound.

TL;DR: This paper considers a variant of the classical two median facility location problem on a tree in which vertices are allowed to have positive or negative weights, and proposes here an O(n log n) algorithm for the MWD problem on trees of arbitrary shape.

TL;DR: It is shown that some algorithms from the collection lead to skeletons based on a particular geometry, corresponding to the (4,8)-median axis, which is a new shape descriptor, featuring nice robustness and conditioning properties.

TL;DR: Sufficient conditions for the existence of Nash equilibria for the considered dynamic noncooperative games are given and polynomial-time algorithms for finding the optimal strategies are elaborated.