19220261
Path protection and blocking probability minimization in optical networks
We study the problem of shared path protection in optical networks from the viewpoint of blocking probability minimization. Unlike the worst-case approach common in other studies, which typically deals with one failure at a time and requires recomputation of the protection paths after every failure, our framework assumes a fixed path protection strategy for every connection that does not change in response to failures in other connections, which is more realistic for networks with high failure rates. We study backup-path strategy configurations that minimize the blocking probability and derive various properties. We show that configurations which do not have partial overlaps among connections backup paths are optimal in a rather general sense. We discuss the minmax optimal configuration properties and present an efficient algorithm for finding it in a case of special interest, while showing it to be NP-hard in general. In addition, we discuss the properties of the game resulting if each connection chooses its backup path selfishly; we show it to belong to the class of potential games, well-studied in the game theory literature, and derive several further properties resulting from its specific structure.
206418940
Residual Analysis for Feature Detection
It is shown that in a very simple form residual analysis achieves results that are at least as good as if not better than those obtained by other techniques. There are many ways for extensions of the method. For example, moving average filters of regularization can be used to obtain the residual images. Also, the strength of the correlation, measured by D/sub rr/(O), can be used to eliminate noise, weak edges, etc. A more ambitious extension is by considering smoothing filters that leave invariant the function representing the reflectance from smooth surfaces. >
11856887
Approximation of linear functionals on a banach space with a Gaussian measure
Abstract We study approximation of linear functionals on separable Banach spaces equipped with a Gaussian measure. We study optimal information and optimal algorithms in average case, probabilistic, and asymptotic settings, for a general error criterion. We prove that adaptive information is not more powerful than nonadaptive information and that μ-spline algorithms, which are linear, are optimal in all three settings. Some of these results hold for approximation of linear operators. We specialize our results to the space of functions with continuous r th derivatives, equipped with a Wiener measure. In particular, we show that the natural splines of degree 2 r + I yield the optimal algorithms. We apply the general results to the problem of integration.
206832588
Optimization problems from feature testing of communication protocols
In feature testing of communication protocols, we want to construct a minimal number of tests with a desirable fault coverage. We model the protocols by extended finite state machines and reduce the test generation process to optimization problems on graphs. We study efficient algorithms and their complexity. We report experimental results on real systems, including Personal HandyPhone System, a 5ESS based ISDN wireless system, and 5ESS Intelligent Network Application Protocol.
46374921
A Formal Specification of the ATM ABR Rate Control Scheme
Abstract Formal specifications are indispensable for computer-aided validation, verification, and testing of communication protocols. However, a large number of practical protocols, including those for ATM, have only informal English specifications. A formal specification helps in achieving a consistent interpretation and thus increases the likelihood of interoperable implementations. As a case study, we consider an important protocol — ATM's Available Bit Rate (ABR) service specification. The ABR source/destination policies have been specified using an English description in the main body of the ATM Forum's draft Traffic Management specification, from which it is hard to conduct a formal analysis. It must be noted however that considerable energy has been spent in providing a reasonably precise specification, while allowing for appropriate implementation latitude. However, an English description still has the potential for different interpretations, which may lead to discrepancy in different vendors' implementations and cause serious problems in interoperability of the communication entities made by different manufacturers. We model the ABR protocols by parameterized communicating extended finite state machines with timers, which is often called a transition system. The protocol is formally specified by the specification of the transitions of the system. We also provide insights gained in the derivation of the formal specification. Furthermore, we introduce a scheduler, involved in transmitting queued cells at the allowed cell rate to meet the minimal requirements from the source/destination protocols. We present the transitions for the source/destination/scheduler machines primarily for transmitting in-rate cells.
31110512
Discontinuity Detection and Thresholding-A Stochastic Approach
We study discontinuity detection and thresholding using a stochastic approach. We discuss a general form of detectors, which includes a number of well known detectors as special cases. Thresholding is indispensable to eliminate spurious responses from the detection process. We propose a Weighted Thresholding, which is designed to cope with a variety of anomalies. Our analysis and experimental results on real images show that intelligent thresholding methods can make a significant difference for discontinuity detection.
15086505
A fast content-based indexing and retrieval technique by the shape information in large image database
Abstract In this paper, we present an efficient content-based image retrieval (CBIR) system which employs the shape information of images to facilitate the retrieval process. For efficient feature extraction, we extract the shape feature of images automatically using edge detection and wavelet transform which is widely used in digital signal processing and image compression. To facilitate speedy retrieval, we also propose the Spherical Pyramid-Technique (SPY-TEC), a new indexing method for similarity search in high-dimensional data space. The SPY-TEC is based on a special space partitioning strategy, which is to divide the d-dimensional data space first into 2d spherical pyramids, and then cut the single spherical pyramid into several spherical slices. This partition provides a transformation of d-dimensional space into 1-dimensional space. Thus, we are able to use a B+-tree to manage the transformed 1-dimensional data. We show that our image indexing method supports faster retrieval than other multi-dimensional indexing methods such as the R*-tree through various experiments. Finally, we show the retrieval effectiveness of our CBIR system using the measure proposed by the QBIC (C. Faloutsos et al., 1994) system.
215179
Two Variations of the Minimum Steiner Problem
Given a set S of starting vertices and a set T of terminating vertices in a graph G = (V,E) with non-negative weights on edges, the minimum Steiner network problem is to find a subgraph of G with the minimum total edge weight. In such a subgraph, we require that for each vertex s$${\in}$$S and t$${\in}$$T, there is a path from s to a terminating vertex as well as a path from a starting vertex to t. This problem can easily be proven NP-hard. For solving the minimum Steiner network problem, we first present an algorithm that runs in time and space that both are polynomial in n with constant degrees, but exponential in |S|+|T|, where n is the number of vertices in G. Then we present an algorithm that uses space that is quadratic in n and runs in time that is polynomial in n with a degree O(max {max {|S|,|T|}−2,min {|S|,|T|}−1}). In spite of this degree, we prove that the number of Steiner vertices in our solution can be as large as |S|+|T|−2. Our algorithm can enumerate all possible optimal solutions. The input graph G can either be undirected or directed acyclic. We also give a linear time algorithm for the special case when min {|S|,|T|} = 1 and max {|S|,|T|} = 2.The minimum union paths problem is similar to the minimum Steiner network problem except that we are given a set H of hitting vertices in G in addition to the sets of starting and terminating vertices. We want to find a subgraph of G with the minimum total edge weight such that the conditions required by the minimum Steiner network problem are satisfied as well as the condition that every hitting vertex is on a path from a starting vertex to a terminating vertex. Furthermore, G must be directed acyclic. For solving the minimum union paths problem, we also present algorithms that have a time and space tradeoff similar to algorithms for the minimum Steiner network problem. We also give a linear time algorithm for the special case when |S| = 1, |T| = 1 and |H| = 2.
6583254
Rectilinear Path Problems among Rectilinear Obstacles Revisited
Efficient algorithms are presented for finding rectilinear collision-free paths between two given points among a set of rectilinear obstacles. The results improve the time complexity of previous results for finding the shortest rectilinear path, the minimum-bend shortest rectilinear path, the shortest minimum-bend rectilinear path and the minimum-cost rectilinear path. For finding the shortest rectilinear path, a graph-theoretic approach is used and an algorithm is obtained with $O(m\log t+ t\log^{3/2} t)$ running time, where $t$ is the number of extreme edges of given obstacles and $m$ is the number of obstacle edges. Based on this result an $O(N\log N+(m+N)\log t + (t+N)\log^2 (t+N))$ running time algorithm for computing the $L_1$ minimum spanning tree of given $N$ terminals among rectilinear obstacles is obtained. For finding the minimum-bend shortest path, the shortest minimum-bend rectilinear path, and the minimum-cost rectilinear path, we devise a new dynamic-searching approach and derive algorithms that run in $O(m\log^2m)$ time using $O(m\log m)$ space or run in $O(m\log^{3/2}m)$ time and space.
2778139
An optimal algorithm for shortest paths on weighted interval and circular-arc graphs, with applications
We give the first linear-time algorithm for computing single-source shortest paths in a weighted interval or circular-arc graph, when we are given the model of that graph, i.e., the actual weighted intervals or circular-arcsand the sorted list of the interval endpoints. Our algorithm solves this problem optimally inO(n) time, wheren is the number of intervals or circular-arcs in a graph. An immediate consequence of our result is anO(qn + n logn)-time algorithm for the minimum-weight circle-cover problem, whereq is the minimum number of arcs crossing any point on the circle; then logn term in this time complexity is from a preprocessing sorting step when the sorted list of endpoints is not given as part of the input. The previously best time bounds were0(n logn) for this shortest paths problem, andO(qn logn) for the minimum-weight circle-cover problem. Thus we improve the bounds of both problems. More importantly, the techniques we give hold the promise of achieving similar (logn)-factor improvements in other problems on such graphs.
5820034
Maximum independent set of a permutation graph in K tracks
A maximum weighted independent set of a permutation graph is a maximum subset of noncrossing chords in a matching diagram (i.e., a set Φ of chords with end-points on two horizontal lines). The problem of finding, among all noncrossing subsets of Φ with density at most k, one with maximum size is considered, where the density of a subset is the maximum number of chords crossing a vertical line and k is a given parameter. A Θ(n log n) time and Θ(n) space algorithm, for solving the problem with n chords, is proposed. As an application, we solve the problem of finding, among all proper subsets with density at most k of an interval graph, one with maximum number of intervals.