Ordinal proportional cost sharing

We consider cost sharing problems with variable demands of heterogeneous goods. We study the compatibility of two axioms imposed on cost sharing methods: ordinality and average cost pricing for homogeneous (ACPH) goods. We generalize the ordinal proportional method (OPM) for the two-agent case, Sprumont [Journal of Economic Theory 81 (1998) 126162] to arbitrary number of agents

An Efficient Dynamic Programming Algorithm for the Generalized LCS Problem with Multiple Substring Exclusion Constrains

In this paper, we consider a generalized longest common subsequence problem with multiple substring exclusion constrains. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a set of $d$ constrains $P=\{P_1,...,P_d\}$ of total length $r$, the problem is to find a common subsequence $Z$ of $X$ and $Y$ excluding each of constrain string in $P$ as a substring and the length of $Z$ is maximized. The problem was declared to be NP-hard\cite{1}, but we finally found that this is not true. A new dynamic programming solution for this problem is presented in this paper. The correctness of the new algorithm is proved. The time complexity of our algorithm is $O(nmr)$.Comment: arXiv admin note: substantial text overlap with arXiv:1301.718

A note on the largest number of red nodes in red-black trees

In this paper, we are interested in the number of red nodes in red-black trees. We first present an $O(n^2\log n)$ time dynamic programming solution for computing $r(n)$, the largest number of red internal nodes in a red-black tree on $n$ keys. Then the algorithm is improved to some $O(\log n)$ time recursive and nonrecursive algorithms. Based on these improved algorithms we finally find a closed-form solution of $r(n)$

Complete Solutions for a Combinatorial Puzzle in Linear Time

In this paper we study a single player game consisting of $n$ black checkers and $m$ white checkers, called shifting the checkers. We have proved that the minimum number of steps needed to play the game for general $n$ and $m$ is $nm + n + m$. We have also presented an optimal algorithm to generate an optimal move sequence of the game consisting of $n$ black checkers and $m$ white checkers, and finally, we present an explicit solution for the general game

Rethinking the Value of Gazetteer in Chinese Named Entity Recognition

Gazetteer is widely used in Chinese named entity recognition (NER) to enhance span boundary detection and type classification. However, to further understand the generalizability and effectiveness of gazetteers, the NLP community still lacks a systematic analysis of the gazetteer-enhanced NER model. In this paper, we first re-examine the effectiveness several common practices of the gazetteer-enhanced NER models and carry out a series of detailed analysis to evaluate the relationship between the model performance and the gazetteer characteristics, which can guide us to build a more suitable gazetteer. The findings of this paper are as follows: (1) the gazetteer improves most of the situations that the traditional NER model datasets are difficult to learn. (2) the performance of model greatly benefits from the high-quality pre-trained lexeme embeddings. (3) a good gazetteer should cover more entities that can be matched in both the training set and testing set.Comment: Accepted by NLPCC 202

An effective fuel level data cleaning and repairing method for vehicle monitor platform

With energy scarcity and environmental pollution becoming increasingly serious, the accurate estimation of fuel consumption of vehicles has been important in vehicle management and transportation planning towards a sustainable green transition. Fuel consumption is calculated by fuel level data collected from high precision fuel level sensors. However, in the vehicle monitor platform, there are many types of error in the data collection and transmission processes, such as the noise, interference, and collision errors are common in the high speed and dynamic vehicle environment. In this paper, an effective method for cleaning and repairing the fuel level data is proposed, which adopts the threshold to acquire abnormal fuel data, the time quantum to identify abnormal data, and linear interpolation based algorithm to correct data errors. Specifically, a modified Gaussian Mixture Model (GMM) based on the synchronous iteration method is proposed to acquire the thresholds, which uses the Particle Swarm Optimization (PSO) algorithm and the steepest descent algorithm to optimize the parameters of GMM. The experiment results based on the fuel level data of vehicles collected over one month prove the modified GMM is superior to GMM-EM on fuel level data, and the proposed method is effective for cleaning and repairing outliers of fuel level data