Catálogo de publicaciones - libros

We consider the following tiling problem: Given a dimensional array of size in each dimension, containing non-negative numbers and a positive integer , partition the array into at most disjoint rectangular subarrays called so as to minimise the maximum weight of any rectangle. The weight of a subarray is the sum of its elements.

In the paper we give a -approximation algorithm that is tight with regard to the only known and used lower bound so far.

Topology-based methods have been successfully used for the analysis and visualization of piecewise-linear functions defined on triangle meshes. This paper describes a mechanism for extending these methods to piecewise-quadratic functions defined on triangulations of surfaces. Each triangular patch is tessellated into monotone regions, so that existing algorithms for computing topological representations of piecewise-linear functions may be applied directly to piecewise-quadratic functions. In particular, the tessellation is used for computing the Reeb graph, which provides a succinct representation of level sets of the function.

We present distributed protocols for electing a leader among mobile agents that are dispersed among the nodes of a graph. While previous solutions for the agent election problem were restricted to specific topologies or under specific conditions, the protocols presented in this paper face the problem in the most general case, i.e. for an arbitrary topology where the nodes of the graph may not be distinctly labelled and the agents might be all identical (and thus indistinguishable from each other). In such cases, the agent election problem is often difficult, and sometimes impossible to solve using deterministic means. We have designed protocols for solving the problem that—unlike previous solutions—are , meaning that they always succeed in electing a leader under any given setting if at all it is possible, and otherwise detect the fact that election is impossible in that setting. We present several election protocols, all effective. Starting with the straightforward solution, that requires an exponential amount of edge-traversals by the agents, we describe significantly more efficient algorithms; in the latter the total number of edge-traversals made by the agents is always polynomial, their difference is in the amount of bits of storage they required at the nodes.

We consider the problem of gathering identical, memoryless, mobile robots in one node of an anonymous unoriented ring. Robots start from different nodes of the ring. They operate in Look-Compute-Move cycles and have to end up in the same node. In one cycle, a robot takes a snapshot of the current configuration (Look), makes a decision to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case makes an instantaneous move to this neighbor (Move). Cycles are performed asynchronously for each robot. For an odd number of robots we prove that gathering is feasible if and only if the initial configuration is not periodic, and we provide a gathering algorithm for any such configuration. For an even number of robots we decide feasibility of gathering except for one type of symmetric initial configurations, and provide gathering algorithms for initial configurations proved to be gatherable.

Recent work on theoretical aspects of steganography resulted in the construction of oracle-based stegosystems. It has been shown that these can be made secure against the steganography equivalents of common cryptographic attacks. In this paper we use methods from complexity theory to investigate the efficiency of sampling from practically relevant types of channels. We show that there are channels that cannot be efficiently used in oracle-based stegosystems. By classifying channels based on their usability for stegosystems, we provide a means to select suitable channels for their practical implementation.