26,490 research outputs found

    Space- and Time-Efficient Algorithm for Maintaining Dense Subgraphs on One-Pass Dynamic Streams

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    While in many graph mining applications it is crucial to handle a stream of updates efficiently in terms of {\em both} time and space, not much was known about achieving such type of algorithm. In this paper we study this issue for a problem which lies at the core of many graph mining applications called {\em densest subgraph problem}. We develop an algorithm that achieves time- and space-efficiency for this problem simultaneously. It is one of the first of its kind for graph problems to the best of our knowledge. In a graph G=(V,E)G = (V, E), the "density" of a subgraph induced by a subset of nodes S⊆VS \subseteq V is defined as ∣E(S)∣/∣S∣|E(S)|/|S|, where E(S)E(S) is the set of edges in EE with both endpoints in SS. In the densest subgraph problem, the goal is to find a subset of nodes that maximizes the density of the corresponding induced subgraph. For any Ï”>0\epsilon>0, we present a dynamic algorithm that, with high probability, maintains a (4+Ï”)(4+\epsilon)-approximation to the densest subgraph problem under a sequence of edge insertions and deletions in a graph with nn nodes. It uses O~(n)\tilde O(n) space, and has an amortized update time of O~(1)\tilde O(1) and a query time of O~(1)\tilde O(1). Here, O~\tilde O hides a O(\poly\log_{1+\epsilon} n) term. The approximation ratio can be improved to (2+Ï”)(2+\epsilon) at the cost of increasing the query time to O~(n)\tilde O(n). It can be extended to a (2+Ï”)(2+\epsilon)-approximation sublinear-time algorithm and a distributed-streaming algorithm. Our algorithm is the first streaming algorithm that can maintain the densest subgraph in {\em one pass}. The previously best algorithm in this setting required O(log⁥n)O(\log n) passes [Bahmani, Kumar and Vassilvitskii, VLDB'12]. The space required by our algorithm is tight up to a polylogarithmic factor.Comment: A preliminary version of this paper appeared in STOC 201

    International Financial Reporting Standards Implementation in Canada: The impact of IFRS Conversion on Canadian Public Banking Enterprises

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    The purpose of the research is developing an understanding of the effect that International Financial Reporting Standards (IFRS) had, if any, on Canadian Publicly Accountable Enterprises (PAEs), specifically their external financial reporting compared to Canadian Generally Accepted Accounting Principles (Canadian GAAP). The focus of this research is the analysis of reported financial ratios of Canadian Banking companies for the year ended December 31, 2010, which will be tested for the statistically-significant differences between Canadian GAAP and IFRS. The research is designed to examine what impact on liquidity, leverage, profitability, and cash flows the change from Canadian GAAP to IFRS has, if any. Overall, the results indicated that there are no statistically significant differences between IFRS and CGAAP means and medians of financial ratios. However, the IFRS conversion did cause significant differences of the leverage ratios under IFRS and CGAAP. The statistical differences were found between medians of IFRS and CGAAP of equity ratios and means of equity’s and debt ratios. The outcomes of the investigation will be useful for Canadian public companies (specifically in the banking industry), investors, stockholders, and other lenders, all of whom rely on financial ratios for various purposes such as credit decisions and debt monitoring. In addition, the United States Government and enterprises in the United States will be able to learn from Canadian experience and make informed decisions about any future changes to accounting standards
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