Dinic has shown that the classic maximum flow problem on a graph of n vertices and m edges can be reduced to a sequence of at most n − 1 so-called ‘blocking flow’ problems on acyclic graphs. For dense graphs, the be...
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Dinic has shown that the classic maximum flow problem on a graph of n vertices and m edges can be reduced to a sequence of at most n − 1 so-called ‘blocking flow’ problems on acyclic graphs. For dense graphs, the best time bound known for the blocking flow problems is O( n 2 ). Karzanov devised the first O( n 2 )-time blocking flow algorithm, which unfortunately is rather complicated. Later Malhotra, Kumar and Maheshwari devise another O( n 2 )-time algorithm, which is conceptually very simple but has some other drawbacks. In this paper we propose a simplification of Karzanov's algorithm that is easier to implement than Malhotra, Kumar and Maheshwari's method.
Background: COVID-19 is an infectious disease caused by SARS-CoV-2. The symptoms of COVID-19 vary from mild-to-moderate respiratory illnesses, and it sometimes requires urgent medication. Therefore, it is crucial to d...
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Background: COVID-19 is an infectious disease caused by SARS-CoV-2. The symptoms of COVID-19 vary from mild-to-moderate respiratory illnesses, and it sometimes requires urgent medication. Therefore, it is crucial to detect COVID-19 at an early stage through specific clinical tests, testing kits, and medical devices. However, these tests are not always available during the time of the pandemic. Therefore, this study developed an automatic, intelligent, rapid, and real-time diagnostic model for the early detection of COVID-19 based on its ***: The COVID-19 knowledge graph (KG) constructed based on literature from heterogeneous data is imported to understand the COVID-19 different relations. We added human disease ontology to the COVID-19 KG and applied a node-embedding graph algorithm called fast random projection to extract an extra feature from the COVID-19 dataset. Subsequently, experiments were conducted using two machine learning (ML) pipelines to predict COVID-19 infection from its symptoms. Additionally, automatic tuning of the model hyperparameters was ***: We compared two graph-based ML models, logistic regression (LR) and random forest (RF) models. The proposed graph-based RF model achieved a small error rate = 0.0064 and the best scores on all performance metrics, including specificity = 98.71%, accuracy = 99.36%, precision = 99.65%, recall = 99.53%, and F1-score = 99.59%. Furthermore, the Matthews correlation coefficient achieved by the RF model was higher than that of the LR model. Comparative analysis with other ML algorithms and with studies from the literature showed that the proposed RF model exhibited the best detection ***: The graph-based RF model registered high performance in classifying the symptoms of COVID-19 infection, thereby indicating that the graph data science, in conjunction with ML techniques, helps improve performance and accelerate innovations.
The outcomes of extensive-form games are the realisation of an exponential number of distinct strategies, which may or may not be Nash equilibria. The aim of this work is to determine whether an outcome of an extensiv...
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The outcomes of extensive-form games are the realisation of an exponential number of distinct strategies, which may or may not be Nash equilibria. The aim of this work is to determine whether an outcome of an extensive-form game can be the realisation of a Nash equilibrium, without recurring to the cumbersome notion of normal-form strategy. We focus on the minimal example of pure Nash equilibria in two-player extensive-form games with perfect information. We introduce a new representation of an extensive-form game as a graph of its outcomes and we provide a new lightweight algorithm to enumerate the realisations of Nash equilibria. It is the first of its kind not to use normal-form brute force. The algorithm can be easily modified to provide intermediate results, such as lower and upper bounds to the value of the utility of Nash equilibria. We compare this modified algorithm to the only existing method providing an upper bound to the utility of any outcome of a Nash equilibrium. The experiments show that our algorithm is faster by some orders of magnitude. We finally test the method to enumerate the Nash equilibria on a new instances library, that we introduce as benchmark for representing all structures and properties of two-player extensive-form games.
As a fundamental and effective tool for document understanding and organization, multi-document summarization enables better information services by creating concise and informative reports for large collections of do...
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As a fundamental and effective tool for document understanding and organization, multi-document summarization enables better information services by creating concise and informative reports for large collections of documents. In this paper, we propose a sentence-word two layer graph algorithm combining with keyword density to generate the multi-document summarization, known as graph ＆ Keywordp. The traditional graph methods of multi-document summarization only consider the influence of sentence and word in all documents rather than individual documents. Therefore, we construct multiple word graph and extract right keywords in each document to modify the sentence graph and to improve the significance and richness of the summary. Meanwhile, because of the differences in the words importance in documents, we propose to use keyword density for the summaries to provide rich content while using a small number of words. The experiment results show that the graph ＆ Keywordp method outperforms the state of the art systems when tested on the Duc2004 data set. Key words： multi-document, graph algorithm, keyword density, graph ＆ Keywordp, Due2004
Given a graph G = (V, epsilon), we want to nd the vertex sets of the components of an unknown subgraph F = (V, E) of G such that E subset of or equal to epsilon. We learn about F by sending an oracle a query set S sub...
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Given a graph G = (V, epsilon), we want to nd the vertex sets of the components of an unknown subgraph F = (V, E) of G such that E subset of or equal to epsilon. We learn about F by sending an oracle a query set S subset of or equal to V, and the oracle tells us the vertices connected to S in F. The objective is to use the minimum number of queries to partition the vertex set V into components of F. In electronic circuit design, the problem is also known as structural diagnosis of wiring networks.
De novo sequencing is one of the most promising proteomics techniques for identification of protein posttranslation modifications (PTMs) in studying protein regulations and functions. We have developed a computer tool...
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De novo sequencing is one of the most promising proteomics techniques for identification of protein posttranslation modifications (PTMs) in studying protein regulations and functions. We have developed a computer tool PRIME for identification of b and y ions in tandem mass spectra, a key challenging problem in de novo sequencing. PRIME utilizes a feature that ions of the same and different types follow different mass-difference distributions to separate b from y ions correctly. We have formulated the problem as a graph partition problem. A linear integer-programming algorithm has been implemented to solve the graph partition problem rigorously and efficiently. The performance of PRIME has been demonstrated on a large amount of simulated tandem mass spectra derived from Yeast genome and its power of detecting PTMs has been tested on 216 simulated phosphopeptides.
This paper presents an algorithm for constructing a cactus representation for ail minimum cuts in an undirected network. Our algorithm runs in O(nm + n(2) log n + gamma m log n) time, where n and m are the number of v...
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This paper presents an algorithm for constructing a cactus representation for ail minimum cuts in an undirected network. Our algorithm runs in O(nm + n(2) log n + gamma m log n) time, where n and m are the number of vertices and edges respectively, and gamma is the number of cycles in a cactus representation, which is the one of the best deterministic time complexities to compute a cactus representation.
We show that, for fixed k, there is a polynomial-time algorithm that finds a maximum (or maximum-weight) stable set in any graph that belongs to the class of k-colorable P-5-free graphs, or, more generally. to the Cla...
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We show that, for fixed k, there is a polynomial-time algorithm that finds a maximum (or maximum-weight) stable set in any graph that belongs to the class of k-colorable P-5-free graphs, or, more generally. to the Class Of P5-free graphs that contain no clique of size k + 1. This is based on the following structural result: every connected k-colorable P5-free graph has a vertex whose non-neighbors induce a (k - 1)-colorable subgraph. (C) 2009 Elsevier B.V. All rights reserved.
This paper deals with broadcasting in a network with t-locally bounded Byzantine faults. One of the simplest broadcasting algorithms under Byzantine failures is referred to as a certified propagation algorithm (CPA), ...
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This paper deals with broadcasting in a network with t-locally bounded Byzantine faults. One of the simplest broadcasting algorithms under Byzantine failures is referred to as a certified propagation algorithm (CPA), which is the only algorithm we know that does not use any global knowledge of the network topology. Hence, it is worth focusing on a graph-theoretic parameter such that CPA will work correctly. Using the theory of maximum adjacency (MA) ordering, a new graph-theoretic parameter for CPA is proposed. Within a factor of two, this parameter approximates the largest t such that CPA works for t-locally bounded Byzantine faults. (C) 2010 Elsevier B.V. All rights reserved.
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