111,006 research outputs found
Parallel and Distributed Algorithms for a Class of Graph-Related Computational Problems.
There exist at least two models of parallel computing, namely, shared-memory and message-passing. This research addresses problems in both these types of systems, and proposes efficient parallel (Shared-Memory Model) and distributed (message-passing) algorithms for a variety of graph related computational problems. In part I, we design algorithms for three generic problems in distributed systems: set manipulation, network structure recognition and facility placement. We present optimal distributed algorithms for recognizing rectangular-mesh networks. The time and message complexity of our algorithm is linear in the number of nodes in the network. We also lay the foundation for the recognition of 2-reducible, outer-planar and cactus graphs. These algorithms have a message complexity of O(kn), where, k is the number of isolated two degree nodes in the network. We introduce the problem of reliable r-domination and design unified optimal distributed algorithms for the total, reliable and independent r-domination on trees. The time and message complexity of our algorithm is O(n), where n is the number of nodes in the tree. In the domain of set manipulation we design optimal algorithms for determining the intersection of sets in a distributed environment, where each processor is assumed to have its own set. The time and message complexity of our set intersection algorithm is O(mn), where m is the cardinality of the smallest set. In part II of our research we design optimal algorithms for r-domination and efficient parallel algorithms for the p-center problems on trees. We also present an optimal algorithm for computing the maximum independent set on intervals i the EREW-PRAM model. The r-domination problem on trees can now be solved in O(logn)time with O(n/logn) processors using the EREW-PRAM model. A parallel algorithm for range searching is developed using the concept of distributed data structures. We show that O(logn) search time can be effected for a range search on n 3-dimensional points using (2.log\sp2n-14.logn + 8) processors. Our algorithm can easily be generalized for the case of d-dimensional range search. (Abstract shortened with permission of author.)
An asynchronous message-passing distributed algorithm for the global critical section problem
This paper considers the global -CS problem which is the problem of
controlling the system in such a way that, at least and at most
processes must be in the CS at a time in the network. In this paper, a
distributed solution is proposed in the asynchronous message-passing model. Our
solution is a versatile composition method of algorithms for -mutual
inclusion and -mutual exclusion. Its message complexity is , where
is the maximum size for the quorum of a coterie used by the algorithm,
which is typically .Comment: This is a modified version of the conference paper in PDAA201
Cell-Probe Lower Bounds from Online Communication Complexity
In this work, we introduce an online model for communication complexity.
Analogous to how online algorithms receive their input piece-by-piece, our
model presents one of the players, Bob, his input piece-by-piece, and has the
players Alice and Bob cooperate to compute a result each time before the next
piece is revealed to Bob. This model has a closer and more natural
correspondence to dynamic data structures than classic communication models do,
and hence presents a new perspective on data structures.
We first present a tight lower bound for the online set intersection problem
in the online communication model, demonstrating a general approach for proving
online communication lower bounds. The online communication model prevents a
batching trick that classic communication complexity allows, and yields a
stronger lower bound. We then apply the online communication model to prove
data structure lower bounds for two dynamic data structure problems: the Group
Range problem and the Dynamic Connectivity problem for forests. Both of the
problems admit a worst case -time data structure. Using online
communication complexity, we prove a tight cell-probe lower bound for each:
spending (even amortized) time per operation results in at best an
probability of correctly answering a
-fraction of the queries
- …