Performance Of Online Algorithm Research Articles

A general framework for handling commitment in online throughput maximization

We study a fundamental online job admission problem where jobs with deadlines arrive online over time at their release dates, and the task is to determine a preemptive single-server schedule which maximizes the number of jobs that complete on time. To circumvent known impossibility results, we make a standard slackness assumption by which the feasible time window for scheduling a job is at least 1+varepsilon times its processing time, for some varepsilon >0. We quantify the impact that different provider commitment requirements have on the performance of online algorithms. Our main contribution is one universal algorithmic framework for online job admission both with and without commitments. Without commitment, our algorithm with a competitive ratio of mathcal {O}(1/varepsilon ) is the best possible (deterministic) for this problem. For commitment models, we give the first non-trivial performance bounds. If the commitment decisions must be made before a job’s slack becomes less than a delta -fraction of its size, we prove a competitive ratio of mathcal {O}(varepsilon /((varepsilon -delta )delta ^2)), for 0<delta <varepsilon . When a provider must commit upon starting a job, our bound is mathcal {O}(1/varepsilon ^2). Finally, we observe that for scheduling with commitment the restriction to the “unweighted” throughput model is essential; if jobs have individual weights, we rule out competitive deterministic algorithms.

New Results on Competitive Analysis of Move To Middle(MTM) List Update Algorithm using Doubly Linked List

On-line algorithm is an emerging area of research since last five decades with immense theoretical and practical significance. Here the sequence of inputs is received and processed by the algorithm one by one in order. At any instant of time, the algorithm has the knowledge of past and present inputs without knowledge of future inputs. Competitive analysis is a standard performance measure for on-line algorithms in which the performance of an on-line algorithm is compared with that of an optimum offline algorithm. List update problem is a well studied research problem in the area of on-line algorithms, which finds applications in data-compression, dictionary maintenance, collision resolution in hash table, symbol table organization in compiler and computing convex hull in computational geometry. From the literature it is known that Move To Front(MTF) is the best performing deterministic list update algorithm using singly linked list in all practical applications. In this paper, we study and analyse the performance of a deterministic on-line list update algorithm known as Move To Middle(MTM) using doubly linked list. We make a first attempt to find the competitive ratio of MTM algorithm, which was only experimentally studied in the literature. In our study by considering doubly linked list as the data structure and a new variant of standard full cost model, we obtain new competitive analysis result and prove that MTM is 2-competitive. From our competitive analysis result, we show that MTM outperforms MTF.

Regret of Multi-Channel Bandit Game in Cognitive Radio Networks

The problem of how to evaluate the rate of convergence to Nash equilibrium solutions in the process of channel selection under incomplete information is studied. In this paper, the definition of regret is used to reflect the convergence rates of online algorithms. The process of selecting an idle channel for each secondary user is modeled as a multi-channel bandit game. The definition of the maximal averaged regret is given. Two existing online learning algorithms are used to obtain the Nash equilibrium for each SU. The maximal averaged regrets are used to evaluate the performances of online algorithms. When there is a pure strategy Nash equilibrium in the multi-channel bandit game, the maximal averaged regrets are finite. A cooperation mechanism is also needed in the process of calculating the maximal averaged regrets. Simulation results show the maximal averaged regrets are finite and the online algorithm with greater convergence rate has less maximal averaged regrets.

Improving the Competitive Ratio of the Online OVSF Code Assignment Problem

Online OVSF code assignment has an important application to wireless communications. Recently, this problem was formally modeled as an online problem, and performances of online algorithms have been analyzed by the competitive analysis. The previous best upper and lower bounds on the competitive ratio were 10 and 5/3, respectively. In this paper, we improve them to 7 and 2, respectively. We also show that our analysis for the upper bound is tight by giving an input sequence for which the competitive ratio of our algorithm is 7 ― ε for an arbitrary constant ε &gt; 0.

An off-line storage allocation algorithm

We investigate the off-line dynamic storage allocation (DSA, for short) problem, as defined in [3, p.226] and [7]. Its basic version is NP-hard in the strong sense as well as many subproblems [3,6]. In this paper we analyze a strongly restricted version of the DSA problem in which block sizes form a divisible sequence and arrivals of larger blocks follow arrivals of smaller ones. We devise a polynomial-time algorithm which finds an optimal allocation for any such instance. This optimum appears to be equal to the maximal amount of busy store at any time in the instance. Hence, the last quantity can be replaced by OPT in Robson's [5] and Krogdahl's [4] lower bounds for the performance of on-line algorithms for the DSA problem. From the obtained estimation it easily follows that no on-line polynomial approximation strategy for DSA achieves a constant worst-case performance ratio. To be precise in discussing on-line and off-line properties of algorithms we formulate the definition of the DSA problem in the way which follows earlier approaches to the problem [5]. This definition is equivalent to that of [3], hence all DSA complexity features remain unchanged. Denote by