This paper addresses the problem of segmenting an image into regions. We define a predicate for measuring the evidence for a boundary between two regions using a graph-based representation of the image. We then develop an efficient segmentation algorithm based on this predicate, and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties. We apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph, and illustrate the results with both real and synthetic images. The algorithm runs in time nearly linear in the number of graph edges and is also fast in practice. An important characteristic of the method is its ability to preserve detail in low-variability image regions while ignoring detail in high-variability regions.

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Efficient Graph-Based Image Segmentation

Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

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The knowledge complexity of interactive proof-systems

The theory of directed graphs has developed enormously over recent decades, yet this book (first published in 2000) remains the only book to cover more than a small fraction of the results. New research in the field has made a second edition a necessity. Substantially revised, reorganised and updated, the book now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems. As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem. Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject. Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science. It will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

Digraphs Theory Algorithms And Applications

Survey: Graph clustering

An additive fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. An additive fuzzy system approximates the function by covering its graph with fuzzy patches in the input-output state space and averaging patches that overlap. The fuzzy system computes a conditional expectation E|Y|X| if we view the fuzzy sets as random sets. Each fuzzy rule defines a fuzzy patch and connects commonsense knowledge with state-space geometry. Neural or statistical clustering systems can approximate the unknown fuzzy patches from training data. These adaptive fuzzy systems approximate a function at two levels. At the local level the neural system approximates and tunes the fuzzy rules. At the global level the rules or patches approximate the function. >

Fuzzy systems as universal approximators

This book documents the state of the art in combinatorial optimization, presenting approximate solutions of virtually all relevant classes of NP-hard optimization problems. The wealth of problems, algorithms, results, and techniques make it an indispensible source of reference for professionals. The text smoothly integrates numerous illustrations, examples, and exercises.

Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties

Complexity and Approximation

We present a fully automatic and weighted dictionary to be used in topical opinion retrieval. We also define a simple topical opinion retrieval function that is free from parameters, so that the retrieval does not need any learning or tuning phase.

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FUB, IASI-CNR and University of Tor Vergata at TREC 2007 Blog Track

The typical online bin-packing problem requires the fitting of a sequence of rationals in (0,1] into a minimum number of bins of unit capacity, by packing the ith input element without any knowledge of the sizes or the number of input elements that follow. Moreover, unlike typical online problems, this one issue does not admit any data reorganization, i.e., no element can be moved from one bin to another. 
In this paper, first of all, the "Relaxed" online bin-packing model will be formalized; this model allows a constant number of elements to move from one bin to another, as a consequence of the arrival of a new input element. 
Then, in the context of this new model, two online algorithms will be described. The first presents linear time and space complexities with a 1.5 approximation ratio and moves, at most once, only "small" elements; the second, instead, is an O(n log n) time and linear space algorithm with a 1.33. . . approximation ratio and moves each element a constant number of times. In the worst case, as a result of the arrival of a new input element, the first algorithm moves no more than three elements, while the second moves as many as seven elements. Please note that the number of movements performed is explicitly considered in the complexity analysis. 
Both algorithms are below the theoretical 1.536. . . lower bound, effective for the online bin-packing algorithms without the movement of elements. Moreover, our algorithms are "more online" than any other linear space online bin-packing algorithm because, unlike the algorithms already known, they allow the return of a (possibly relevant) fraction of bins before the work is carried out.

Algorithms for the Relaxed Online Bin-Packing Model

: We take part in the opinion and polarity retrieval tasks of the blog track. A test collection, called Blog06, was created for the blog track in 2006 with three main different components: feeds, permalinks and home-pages. The collection contains spam as well as possibly no blogs and no english pages. For our experimentation only permalinks have been taken into consideration, consisting of 3.2 million of Web pages for a total of 88.8GB, each one containing a post and its related comments. The evaluation metrics are precision/recall based, the Mean Average Precision (MAP) and R-Precision (RPrec), but we also focused on Precision at 10 (P@10), due to its relevance in evaluating the effectiveness of Web search engines. As in 2007, we based our approach on the construction of ad-hoc weighted dictionaries, containing terms assumed to be used to express a sentiment. The weight is a measure of how much sentiment the term expresses. To automatically construct our dictionaries, we assumed that opinion-bearing words distribute more randomly in the set of opinionated documents than semantic-bearing terms, but less randomly than not-informative terms.

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Giorgio Gambosi

Papers

Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties

Complexity and Approximation

FUB, IASI-CNR and University of Tor Vergata at TREC 2007 Blog Track

Algorithms for the Relaxed Online Bin-Packing Model

FUB, IASI-CNR and University of Tor Vergata at TREC 2008 Blog Track