Maximum Weight Path Research Articles

Foreign Language Teaching and Learning Behaviour with a Big Data Corpus

Abstract This paper firstly constructs a foreign language subject system according to the foreign language teaching objectives and students’ learning situation in colleges and universities, puts forward a policy of informatization of foreign language teaching, and summarizes the ways in which college students’ foreign language learning behavior in the era of big data. Secondly, on the basis of corpus technology, the word vectorization representation of foreign language utterances is carried out, followed by similarity calculation of the word vectorization representation, judging the type of foreign language learning according to the results of foreign language semantic similarity calculation, and calculating the maximum weight path of the word vector sequence by using dynamic planning algorithm. Then, according to the demand analysis of the foreign language teaching corpus, the foreign language teaching corpus is constructed, and the application analysis of the corpus of foreign language teaching is carried out. The results indicate that the students in both classes have a similar understanding of the meaning and lexical properties of vocabulary. However, there is a certain gap in the collocation and utilization of vocabulary, and the corpus-based vocabulary teaching method is more conducive to students’ mastery of the target vocabulary than the traditional vocabulary teaching method, and the level of vocabulary learning is comparatively higher and more effective. The quality of foreign language teaching in colleges and universities can be improved by reference to this study.

Accurate summary-based cardinality estimation through the lens of cardinality estimation graphs

This paper is an experimental and analytical study of two classes of summary-based cardinality estimators that use statistics about input relations and small-size joins in the context of graph database management systems: (i) optimistic estimators that make uniformity and conditional independence assumptions; and (ii) the recent pessimistic estimators that use information theoretic linear programs (LPs). We begin by analyzing how optimistic estimators use pre-computed statistics to generate cardinality estimates. We show these estimators can be modeled as picking bottom-to-top paths in a cardinality estimation graph (CEG), which contains sub-queries as nodes and edges whose weights are average degree statistics. We show that existing optimistic estimators have either undefined or fixed choices for picking CEG paths as their estimates and ignore alternative choices. Instead, we outline a space of optimistic estimators to make an estimate on CEGs, which subsumes existing estimators. We show, using an extensive empirical analysis, that effective paths depend on the structure of the queries. While on acyclic queries and queries with small-size cycles, using the maximum-weight path is effective to address the well known underestimation problem, on queries with larger cycles these estimates tend to overestimate, which can be addressed by using minimum weight paths. We next show that optimistic estimators and seemingly disparate LP-based pessimistic estimators are in fact connected. Specifically, we show that CEGs can also model some recent pessimistic estimators. This connection allows us to adopt an optimization from pessimistic estimators to optimistic ones, and provide insights into the pessimistic estimators, such as showing that they have combinatorial solutions.

Mobility-Driven Association Policies for Dense Wireless Networks

The primary approach to increase coverage and capacity in infrastructure-based wireless networks is densification. Densification, however, presents a major challenge when serving mobile users, which is the overhead associated with the increased rate of base station handovers. Assuming a prior knowledge of a mobile’s trajectory and base stations’ locations, we formulate the problem of determining the sequence of handovers that optimize the trade-off between the mobile user’s perceived throughput and handover overheads in noise-limited environments. Under appropriate conditions, we show that the problem reduces to determining a maximum weight path in a directed acyclic graph induced by the mobile user’s trajectory. In practice, knowledge of a mobiles’ trajectory may be limited and one may also want to limit the handover complexity, whence we propose a new class of mobility-driven greedy association policies. The greedy policies are based on defining a handover support set, which constrains both the possible handovers and the complexity/information requirements. In a setting where base station locations follow a Poisson point process, we show that the performance of such handover processes follows a continuous-time Markov process which can be analyzed using complex variable techniques. This enables one to explore the optimization size/shape of the handover support set for mobility-driven greedy handover strategies and their relative performance compared to traditional association policies.

Dynamic Range Reduction of SAR Image via Global Optimum Entropy Maximization With Reflectivity-Distortion Constraint

The visualization of synthetic aperture radar (SAR) images plays a critical role in remote sensing applications. To effectively obtain the image suitable for human observation, this paper introduces a new SAR image visualization algorithm to map the high dynamic range SAR amplitude values to low dynamic range displays via reflectivity distortion preserved entropy maximization. Its designed objective is to present the maximal amount of information content in the displayed image, and being optimal in an information theoretical sense, as well as restricting the upper bound of the reflection distortion caused by tone mapping. The resulting optimization problem can be graph theoretically modeled as a $K$ -edges maximum weight path problem in a directed acyclic graph, and it can be solved efficiently by dynamic programming in real time. Empirical evidences are provided to demonstrate the superior visual quality obtained by our new visualization technique.

On the longest path of a randomly weighted tournament

Finding a maximum weight path in a directed or undirected graph is a basic combinatorial and algorithmic problem. We consider this problem for tournaments in the well-studied random weighted model. Denote by P(G,D) the probability space obtained by independently assigning weights to the edges of a tournament G according to a nonnegative probability distribution D. Denote by ℓ(G,D) the expected weight of a path with maximum weight.If D has finite mean μ, then ℓ(G,D)≥μ(n−1) is a trivial lower bound, with equality if D is constant, as by Redei’s Theorem, every tournament has a Hamilton path. However, already for very simple nontrivial distributions, it is challenging to determine ℓ(G,D) even asymptotically, and even if the tournament is small and fixed. We consider the two natural distributions of the random weighted model, the continuous uniform distribution U[0,1] and the symmetric Bernoulli distribution U{0,1}. Our first result is that for any tournament, both ℓ(G,U{0,1}) and ℓ(G,U[0,1]) are larger than the above trivial 0.5(n−1) lower bound in the sense that 0.5 can be replaced by a larger constant. To this end we prove the existence of dense partial squares of Hamilton paths in any tournament, a combinatorial result which seems of independent interest. Regarding upper bounds, while for some tournaments one can prove that both ℓ(G,U{0,1}) and ℓ(G,U[0,1]) are n−o(n), we prove that there are other tournaments for which both ℓ(G,U{0,1}) and ℓ(G,U[0,1]) are significantly smaller. In particular, for every n, there are n-vertex tournaments for which ℓ(G,U{0,1})≤0.614(n−1). Finally, we state several natural open problems arising in this setting.

Общий подход к решению задач на графах коллективом автоматов

We propose a general method to solve graph problems by a set of automata (computational agents) located in vertices of undirected ordered connected rooted graph and communicating by passing messages along graph edges. The automata are semi-robots, i.e., their internal memory size is sufficient to store values depending on the number of vertices and edges of the graph (n and m, correspondingly) but is too small to store the complete graph description. Section 2 presents classification of graph-based distributed computational models depending on internal memory size of vertex automaton, vertex automaton operation time, and edge capacity (the number of messages that are passing along an edge simultaneously). We choose for further use the model of maximum parallelism, having zero automaton operation time and unbounded edge capacity. It allows to obtain lower complexity bounds on distributed graph problems. Section 3 describes algorithm complexity assessment rules. Section 4 presents basic message processing procedures and message classification according to paths passed by them and methods of message processing by vertex automaton. We propose to construct algorithms solving graph problems on the base of the procedures considered, and present some examples in further sections. Sections 5-9 describe distributed algorithms for spanning tree construction, for task termination detection (based on detection of absence of messages used by the task), for shortest paths tree construction, for graph vertices enumeration, for collecting graph structure information in the root automaton memory (if it is unbounded). The algorithms proposed has linear time complexity in n and m, and use linear in n and m number of messages. Section 10 considers construction of maximum weight path in a weighted graph, which is the NP problem. We propose the algorithm that for the sake of using unbounded number of messages can solve this problem in linear time in n and m. The conclusion summarizes the paper and draws directions of further research: constructing algorithms for other graph problems and generalization of the approach to directed, non-deterministic and dynamic graphs.

Image Enhancement by Entropy Maximization and Quantization Resolution Upconversion

This article introduces a new contrast enhancement algorithm of tone-preserving entropy maximization. Its design objective is to present the maximal amount of information content in the enhanced image, or being optimal in an information theoretical sense, while preventing the loss of tone continuity. The resulting optimization problem can be graph theoretically modeled as the construction of the $K$ -edges maximum-weight path, and it can be solved efficiently by dynamic programming. Moreover, the proposed algorithm is made more effective by being combined with a preprocess of image restoration that aims to correct quantization errors caused by the analog-to-digital conversion of image signals. Empirical evidences are provided to demonstrate the superior visual quality obtained by the new image enhancement algorithm.

Discrete models and algorithms for packet scheduling in smart antennas

Abstract We investigate two combinatorial optimization problems arising when scheduling packets in a smart antenna. To select a maximum number of users to be simultaneously served in a given time slot, an arc-circular model is proposed and a polynomial algorithm, which searches for a maximum weight path in an appropriate acyclic graph, is presented. To partition the users so mimimize the number of time slots needed to transmit all the given packets, heuristics are developed.