Designing Efficient Parallel Algorithms for Graph Problems

Graph algorithms are concerned with the algorithmic aspects of solving graph problems. The problems are motivated from and have application to diverse areas of computer science, engineering and other disciplines. Problems arising from these areas of application are good candidates for parallelization since they often have both intense computational needs and stringent response time requirements. Motivated by these concerns, this thesis investigates parallel algorithms for these kinds of graph problems that have at least one of the following properties: the problems involve some type of dynamic updates; the sparsification technique is applicable; or the problems are closely related to communications network issues. The models of parallel computation used in our studies are the Parallel Random Access Machine (PRAM) model and the practical interconnection network models such as meshes and hypercubes. ¶ ..

Structure and function in flow networks

Peer reviewedPublisher PD

Study of Routing Protocols in Telecommunication Networks

In this paper we have discussed the problem of routing in telecommunication networks and the salient characteristics of some of the most popular routing schemes. In particular, we have discussed the characteristics of adaptive and multipath routing solutions versus static and single-path strategies

Network Flows

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Polynomial fixed-parameter algorithms : a case study for longest path on interval graphs.

We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus on a fundamental graph problem: Longest Path; it is NP-hard in general but known to be solvable in O(n^4) time on n-vertex interval graphs. We show how to solve Longest Path on Interval Graphs, parameterized by vertex deletion number k to proper interval graphs, in O(k^9n) time. Notably, Longest Path is trivially solvable in linear time on proper interval graphs, and the parameter value k can be approximated up to a factor of 4 in linear time. From a more general perspective, we believe that using parameterized complexity analysis for polynomial-time solvable problems offers a very fertile ground for future studies for all sorts of algorithmic problems. It may enable a refined understanding of efficiency aspects for polynomial-time solvable problems, similarly to what classical parameterized complexity analysis does for NP-hard problems

Destination-based Routing and Circuit Allocation for Future Traffic Growth

Internet traffic continues to grow relentlessly, driven largely by increasingly high- \\ resolution video streaming, the increasing adoption of cloud computing, the emergence of 5G networks, and the ever-growing reach of social media and social networks. Existing networks use packet switching to route packets on a hop-by-hop basis from the source to the destination. However, they suffer from two shortcomings. First, in existing networks, packets are routed along a fixed shortest path using the Open Shortest Path First (OSPF) protocol or obliviously load-balanced across equal-cost paths using the Equal-Cost Multi-Path (ECMP) protocol. These routing protocols do not fully utilize the network capacity because they do not adapt to network congestions in their routing decisions. Second, although studies have shown that the majority of packets processed by Internet routers are pass-through traffic, packets nonetheless have to be queued and routed at every hop in existing networks, which unnecessarily adds substantial delays and processing costs.In this thesis, we present two new approaches to overcome these shortcomings. First, we propose new backpressure-based routing algorithms which use only shortest-path routes when they are sufficient to accommodate the given traffic load, but will incrementally expand routing choices as needed to accommodate increasing traffic loads. This avoids the poor delay performance inherent in backpressure-based routing algorithms where packets may take long detours under light or moderate loads, and still retains the notable advantage, the network-wide optimal throughput, because packets are adaptively routed along less congested paths.Second, we propose a unified packet and circuit switched network in which the underlying optical transport is used to circuit-switch pass-through traffic by means of pre-established circuits. This avoids unnecessary packet queuing delays and processing costs at each hop. We propose a novel convex optimization framework based on a new destination-based multicommodity flow formulation for the allocation of circuits in such unified networks