Efficient approximation algorithms for the bounded flexible scheduling problem in clouds

Clouds, such as Amazon Infrastructure-as-a-Service (IaaS) clouds and EMC Hybrid Cloud, impose growing requirements of resource-efficiency scheduling. The bounded flexible scheduling (BFS) problem is one of the problems proposed to meet such requirements. In BFS, we are given a set of identical machines and a set of jobs, each of which is with a value, a workload, a deadline and a parallelism degree, i.e., the maximum number of machines on which the job can execute concurrently. The problem is to compute an assignment of the given jobs to the machines, such that the total value of the jobs successfully completed by their deadlines is maximized. This paper presents a factor C/C-k approximation algorithm for BFS, where k is the maximum parallelism degree and C is the capacity of the system (i.e., the number of machines). Since C ≫ k in BFS, our result significantly improves the known best approximation ratio of (2C-k/C-k)(1-ϵ) for tight deadlines [17], and C/C-k · s/s-1/s for loose deadlines [18] on a slackness ratios > 1 that is the maximum ratio between a job's earliest actual finish time and its deadline. We first propose feasibility condition to determine whether an instance of BFS is feasible, i.e., whether there exists a scheduling according to which all jobs can finish before their deadlines, which is the key to achieve the ratio improvement of our algorithm. To prove the correctness of the feasibility condition, we give a simple linear program (LP) for a weaker version of BFS, and show that it is with an integral polyhedron and hence the version of BFS is polynomial-time solvable. Then we present a greedy algorithm and its equivalent primal-dual algorithm for the complementary problem of BFS. Both algorithms have an approximation ratio of C/C-k, and time complexity O(n² + nT), where n is the number of jobs and T is the number of time slots. As a by-product, we show that the BFS admits a polynomial-time approximation scheme (PTAS) when T is fixed.Longkun Guo and Hong She

Disruptive Innovation Within the Legal Services Ecosystem

Most law firms have done little to address the opportunities and threats related to potentially disruptive technology (DT), such as artificial intelligence (AI) and machine learning (ML). The purpose of this multiple case study was to explore strategies that law firm leaders in the United States used to address the potentially detrimental influences of DT, such as AI and ML, on their organizations. The systems approach to management was employed as the conceptual framework. Data were collected from 6 participants at 2 international law firms with offices in California using semistructured interviews and organizational artifacts. Data were analyzed using Miles, Huberman, and Saldana\u27s data analysis method, resulting in 4 themes: recognizing the legal ecosystem and legal firms are open systems, but organizational subsystems often function as semiclosed systems; acknowledging that while DT represents the most significant potential challenge in the near future, the immediate challenge is improving technology, which requires organizational adjustments; recognizing the need for firms to invest more heavily in innovation generation activities; and realizing the need for increased utilization of augmenting technologies, such as AI or ML, to streamline nonadvisory outputs. The findings of this study might support best practices for addressing DT and contribute to social change by outlining ways in which firms can lower costs to clients while increasing access to legal services for those in underserved communities