Algorithms on Evolving Graphs

Today's applications process large scale graphs which are evolving in nature. We study new com- putational and data model to study such graphs. In this framework, the algorithms are unaware of the changes happening in the evolving graphs. The algorithms are restricted to probe only lim- ited portion of graph data and are expected to produce a solution close to the optimal one and that too at each time step. This frameworks assumes no constraints on resources like memory and computation time. The limited resource for such algorithms is the limited portion of graph that is allowed to probe (e.g. the number of queries an algorithm can make in order to learn about the graph). We apply this framework to two classical graph theory problems: Shortest Path problem and Maximum Flow problem. We study the way algorithm behaves under evolving model and how does the evolving nature of the graph aects the solution given by the algorithm

Sorting and Selection on Dynamic Data ∗

We formulate and study a new computational model for dynamic data. In this model, the data changes gradually and the goal of an algorithm is to compute the solution to some problem on the data at each time step, under the constraint that it only has limited access to the data each time. As the data is constantly changing and the algorithm might be unaware of these changes, it cannot be expected to always output the exact right solution; we are interested in algorithms that guarantee to output an approximate solution. In particular, we focus on the fundamental problems of sorting and selection, where the true ordering of the elements changes slowly. We provide algorithms with performance close to the optimal in expectation and with high probability.

Sorting and selection on dynamic data

We formulate and study a new computational model for dynamic data. In this model, the data changes gradually and the goal of an algorithm is to compute the solution to some problem on the data at each time step, under the constraint that it only has limited access to the data each time. As the data is constantly changing and the algorithm might be unaware of these changes, it cannot be expected to always output the exact right solution; we are interested in algorithms that guarantee to output an approximate solution. In particular, we focus on the fundamental problems of sorting and selection, where the true ordering of the elements changes slowly. We provide algorithms with performance close to the optimal in expectation and with high probability. (C) 2010 Elsevier B.V. All rights reserved