1746401
On the Effective Enumerability of NP Problems
In the field of computational optimization, it is often the case that we are given an instance of an NP problem and asked to enumerate the first few best solutions to the instance. Motivated by this, we propose in this paper a new framework to measure the effective enumerability of NP optimization problems. More specifically, given an instance of an NP problem, we consider the parameterized problem of enumerating a given number of best solutions to the instance, and study its average complexity in terms of the number of solutions. Our framework is different from the previously-proposed ones. For example, although it is known that counting the number of k-paths in a graph is #W[1]-complete, we present a fixed-parameter enumeration algorithm for the problem. We show that most algorithmic techniques for fixed-parameter tractable problems, such as search trees, color coding, and bounded treewidth, can be used for parameterized enumerations. In addition, we design elegant and new enumeration techniques and show how to generate small-size structures and enumerate solutions efficiently.
9458829
Face Tracing Based Geographic Routing in Nonplanar Wireless Networks
Scalable and efficient routing is a main challenge in the deployment of large ad hoc wireless networks. An essential element of practical routing protocols is their accommodation of realistic network topologies. In this paper, we study geographic routing in general large wireless networks. Geographic routing is a celebrated idea that uses the locations of nodes to effectively support routing. However, to guarantee delivery, recent geographic routing algorithms usually resort to perimeter routing, which requires the removal of communication links to get a planar sub-network on which perimeter routing is performed. Localized network planarization requires the wireless network to be a unit-disk graph (UDG) or its close approximation. For networks that significantly deviate from the UDG model, a common case in practice, substantially more expensive and non-localized network planarization methods have to be used. How to make such methods efficiently adaptable to network dynamics, and how to avoid the removal of an excessive number of links that leads to lowered routing performance, are still open problems. To enable efficient geographic routing in general wireless networks, we present face-tracing based routing, a novel approach that routes the message in the faces of the network that are virtually embedded in a topological surface. Such faces are easily recognizable and constructible, and adaptively capture the important geometric features in wireless networks - in particular, holes, -thus leading to very efficient routing. We show by both analysis and si mulations that the face-tracing based routing is a highly scalable routing protocol that generates short routes, incurs low overhead, adapts quickly to network dynamics, and is very robust to variations in network models.
2376990
Power-aware processor scheduling under average delay constraints
In this paper, voltage scaling strategies for scheduling aperiodic tasks under average delay constraints are studied. Dynamic voltage scaling in single processor systems is formulated as a constrained stochastic optimization problem for which the optimal solution can be obtained using a combination of Lagrange relaxation and the value iteration method. For multiprocessor systems, we present a two-phase approach. In the first phase, the speed settings and static workload distribution of the processors are optimized to minimize the total power dissipation. Dynamic voltage scaling techniques are then applied to each individual processor in the second phase. Both homogeneous and heterogeneous systems have been investigated. Based on queueing theory, the proposed algorithms guarantee conformity to the average delay constraint. Moreover, our simulation experiments have shown they are effective for minimizing power consumption.
52810037
A Riemannian Weighted Filter for Edge-sensitive Image Smoothing
This paper describes a new method for image smoothing. We view the image features as residing on a differential manifold, and we work with a representation based on the exponential map for this manifold (i.e. the map from the manifold to a plane that preserves geodesic distances). On the exponential map we characterise the features using a Riemannian weighted mean. We show how both gradient descent and Newton's method can be used to find the mean. Based on this weighted mean, we develop an edge-preserving filter that combines Gaussian and median filters of gray-scale images. We demonstrate our algorithm both on direction fields from shape-from-shading and tensor-valued images
204989114
On the numbers of spanning trees and Eulerian tours in generalized de Bruijn graphs
Abstract In this paper, we give the spectra and characteristic polynomials of generalized de Bruijn graphs. By Tutte's Theorem we can obtain the number of spanning trees and the number of Eulerian tours in such graphs.
46427487
The Clar Covering Polynomial of Hexagonal Systems I
Abstract In this paper the Clar covering polynomial of a hexagonal system is introduced. In fact it is a kind of F polynomial [4] of a graph, and can be calculated by recurrence relations. We show that the number of aromatic sextets (in a Clar formula), the number of Clar formulas, the number of Kekule structures and the first Herndon number for any Kekulean hexagonal system can be easily obtained by its Clar covering polynomial. In addition, we give some theorems to calculate the Clar covering polynomial of a hexagonal system. As examples we finally derive the explicit expressions of the Clar covering polynomials for some small hexagonal systems and several types of catacondensed hexagonal systems. A relation between the resonance energy and the Clar covering polynomial of a hexagonal system is considered in the next paper.
32475390
k-Cycle resonant graphs
Abstract A connected graph G is said to be k -cycle resonant if, for 1 ⩽ t ⩽ k , any t disjoint cycles in G are mutually resonant, that is, there is a perfect matching M of G such that each of the t cycles is an M -alternating cycle. In this paper, we at the first time introduce the concept of k -cycle resonant graphs, and investigate some properties of k -cycle resonant graphs. Some simple necessary and sufficient conditions for a graph to be k -cycle resonant are given. The construction of k -cycle resonant hexagonal systems are also characterized.