Derandomization of Online Assignment Algorithms for Dynamic Graphs

This paper analyzes different online algorithms for the problem of assigning weights to edges in a fully-connected bipartite graph that minimizes the overall cost while satisfying constraints. Edges in this graph may disappear and reappear over time. Performance of these algorithms is measured using simulations. This paper also attempts to derandomize the randomized online algorithm for this problem

Online Assignment Algorithms for Dynamic Bipartite Graphs

This paper analyzes the problem of assigning weights to edges incrementally in a dynamic complete bipartite graph consisting of producer and consumer nodes. The objective is to minimize the overall cost while satisfying certain constraints. The cost and constraints are functions of attributes of the edges, nodes and online service requests. Novelty of this work is that it models real-time distributed resource allocation using an approach to solve this theoretical problem. This paper studies variants of this assignment problem where the edges, producers and consumers can disappear and reappear or their attributes can change over time. Primal-Dual algorithms are used for solving these problems and their competitive ratios are evaluated

Simultaneously Load Balancing for Every p-norm, With Reassignments

This paper investigates the task of load balancing where the objective function is to minimize the p-norm of loads, for pgeq 1, in both static and incremental settings. We consider two closely related load balancing problems. In the bipartite matching problem we are given a bipartite graph G=(Ccup S, E) and the goal is to assign each client cin C to a server sin S so that the p-norm of assignment loads on S is minimized. In the graph orientation problem the goal is to orient (direct) the edges of a given undirected graph while minimizing the p-norm of the out-degrees. The graph orientation problem is a special case of the bipartite matching problem, but less complex, which leads to simpler algorithms. For the graph orientation problem we show that the celebrated Chiba-Nishizeki peeling algorithm provides a simple linear time load balancing scheme whose output is an orientation that is 2-competitive, in a p-norm sense, for all pgeq 1. For the bipartite matching problem we first provide an offline algorithm that computes an optimal assignment. We then extend this solution to the online bipartite matching problem with reassignments, where vertices from C arrive in an online fashion together with their corresponding edges, and we are allowed to reassign an amortized O(1) vertices from C each time a new vertex arrives. In this online scenario we show how to maintain a single assignment that is 8-competitive, in a p-norm sense, for all pgeq 1

Load Balancing for Dynamic Clients, Game Theory Approach

We address the problem of load balancing which is considered as a technique to spread work between two or more computers in order to get optimal response time and resource utilization between servers by using Nash equilibrium which is the central concern of game theory. We use a normal form table to express the payoff for every client, every client has estimate time for execution and every server has speed, from these facts, we innovate a dynamic payoff matrix to evaluate a Nash equilibrium point and then determine which server can serve an appropriate client to achieve best load balancing which is called "server matching" (Each client is matched to exactly one server, but a server can be matched to multiple clients or none.). We use Netlogo simulation to implement this matching, besides a useful game theory oolset called GAMBIT (Gambit toolset homepage, 2005) to solve the payoff matrix and compute Nash equilibrium point. This paper was done between the years 2007 – 2009, and to know what was done in this paper we can argue that we contribute in accomplishing the load balancing between servers, using new technique depends on game theory perspective, for that reason we can answer the question why this thesis was done, because it is very vital in achieving this goal. We use in our thesis a simulation methodology to prove the results that we have obtained from the simulation program which is a Netlogo V4.0.2, and we compare the results with traditionally techniques in load balancing. Finally, the results show that we improve the performance for the whole system by 4% in achieving load balancing and overweight the possibilities of using this technique in real system around the world