Within the broad ambit of algorithm design, the study of dynamic graph algorithms continues to be a thriving area of research. Commensurate with this interest is an extensive literature on the topic. Not surprisingly,...
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Within the broad ambit of algorithm design, the study of dynamic graph algorithms continues to be a thriving area of research. Commensurate with this interest is an extensive literature on the topic. Not surprisingly, dynamic algorithms for all varieties of shortest path problems, in view of their practical importance, occupy a preeminent position. Relevant to this paper are fully dynamic algorithms for chordal graphs. Surprisingly, to the best of our knowledge, there seems to be no reported results for the problem of dynamic algorithms for strongly chordal graphs. To redress this gap, in this paper, we propose a semi-dynamic algorithm for edge-deletions and a semi-dynamic algorithm for edge-insertions in a strongly chordal graph, G. The query complexity of an edge-deletion is O(d(u)(2)d(v)(2)), where d(u) and d(v) are the degrees of the vertices u and v of the candidate edge {u,v}, while the query complexity of an edge-insertion is O(n(2)), where n is the number of vertices of G.
The importance of skyline and dominance relationship analysis has been well recognized in multicriteria decision-making applications. In this paper, we propose the problem of "Finding Skyline with Customer Prefer...
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ISBN:
(纸本)9781509001897
The importance of skyline and dominance relationship analysis has been well recognized in multicriteria decision-making applications. In this paper, we propose the problem of "Finding Skyline with Customer Preferences and Cost Constraints", which utilizes the concept of dominance for business analysis from a microeconomic perspective. Our problem aims to discover the dominance relationship between products and potential customers. Given a set of customer preferences, we want to help the company to design set of competitive products so that the products can satisfy as many customer requirements as possible and the cost of producing the products is within a specified threshold. By "competitive products" we mean that the products cannot be dominated by other products in the market. We formally define the problem and discuss the difficulty of the problem. We also present the foundation and the intuition of our pruning methods. Then we proposed three efficient algorithms that utilize our pruning methods to address the problem. In addition, we also prove the correctness of our proposed algorithms.
The focus of this special issue is optimization methods for problems whose solutions have simple *** structures include sparsity (the solution has very few nonzero entries),low-rankness (the solution is a matrix of ve...
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The focus of this special issue is optimization methods for problems whose solutions have simple *** structures include sparsity (the solution has very few nonzero entries),low-rankness (the solution is a matrix of very low rank),consensus (the solution is a set of identical vectors),and *** authors of the articles in this special issue use certain functions and constraints to ensure their solutions to have these *** functions are typically nonsmooth,and such constraints involve all components of variables,thus posing a challenge to algorithm *** algorithms using (sub)gradients and projections are either non-applicable or performing ***,the authors study new methods for better efficiency.
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