Pavel Ghosh

Energy efficient application mapping to NoC processing elements operating at multiple voltage levels

An efficient technique for mapping application tasks to heterogeneous processing elements (PEs) on a Network-on-Chip (NoC) platform, operating at multiple voltage levels, is presented in this paper. The goal of the mapping is to minimize energy consumption subject to the performance constraints. Such a mapping involves solving several subproblems. Most of the research effort in this area often address these subproblems in a sequential fashion or a subset of them. We take a unified approach to the problem without compromising the solution time and provide techniques for optimal and heuristic solutions. We prove that the voltage assignment component of the problem itself is NP-hard and is inapproximable within any constant factor. Our optimal solution utilizes a Mixed Integer Linear Program (MILP) formulation of the problem. The heuristic utilizes MILP relaxation and randomized rounding. Experimental results based on E3S benchmark applications and a few real applications show that our heuristic produces near-optimal solution in a fraction of time needed to find the optimal.

Beyond connectivity - new metrics to evaluate robustness of networks

Robustness or fault-tolerance capability of a network is an important design parameter in both wired and wireless networks. Connectivity of a network is traditionally considered to be the primary metric for evaluation of its fault-tolerance capability. However, connectivity κ(G) (for random faults) or region-based connectivity κR(G) (for spatially correlated or region-based faults, where the faults are confined to a region R) of a network G, does not provide any information about the network state, (i.e., whether the network is connected or not) once the number of faults exceeds κ(G) or κR(G). If the number of faults exceeds κ(G) or κR(G), one would like to know, (i) the number of connected components into which G decomposes, (ii) the size of the largest connected component, (iii) the size of the smallest connected component. In this paper, we introduce a set of new metrics that computes these values. We focus on one particular metric called region-based component decomposition number (RBCDN), that measures the number of connected components in which the network decomposes once all the nodes of a region fail. We study the computational complexity of finding RBCDN of a network. In addition, we study the problem of least cost design of a network with a target value of RBCDN. We show that the optimal design problem is NP-complete and present an approximation algorithm with a performance bound of O(log K + 4log n), where n denotes the number of nodes in the graph and K denotes a target value of RBCDN. We evaluate the performance of our algorithm by comparing it with the performance of the optimal solution. Experimental results demonstrate that our algorithm produces near optimal solution in a fraction of time needed to find an optimal solution.

Resource mapping and scheduling for heterogeneous network processor systems

Task to resource mapping problems are encountered during (i) hardware-software co-design and (ii) performance optimization of Network Processor systems. The goal of the first problem is to find the task to resource mapping that minimizes the design cost subject to all design constraints. The goal of the second problem is to find the mapping that maximizes the performance, subject to all architectural constraints. To meet the design goals in performance, it may be necessary to allow multiple packets to be inside the system at any given instance of time and this may give rise to the resource contention between packets. In this paper, a Randomized Rounding (RR) based solution is presented for the task to resource mapping and scheduling problem. We also proposed two techniques to detect and eliminate the resource contention. We evaluate the efficacy of our RR approach through extensive simulation. The simulation results demonstrate that this approach produces near optimal solutions in almost all instances of the problem in a fraction of time needed to find the optimal solution. The quality of the solution produced by this approach is also better than often used list scheduling algorithm for task to resource mapping problem. Finally, we demonstrate with a case study, the results of a Network Processor design and scheduling problem using our techniques.

Efficient mapping and voltage islanding technique for energy minimization in NoC under design constraints

Voltage islanding technique in Network-on-Chip (NoC) can significantly reduce the computational energy consumption by scaling down the voltage levels of the processing elements (PEs). This reduction in energy consumption comes at the cost of the energy consumption of the level shifters between voltage islands. Moreover, from physical design perspective it is desirable to have a limited number of voltage islands. Considering voltage islanding during mapping of the PEs to the NoC routers can significantly reduce both the computational and the level-shifter energy consumptions and the communication energy consumption on the NoC links. In this paper, we formulate the problem as an optimization problem with an objective of minimizing the overall energy consumption constrained by the performance in terms of delay and the maximum number of voltage islands. We provide the optimal solution to our problem using Mixed Integer Linear Program (MILP) formulation. We also propose a heuristic based on random greedy selection to solve the problem. Experimental results using E3S benchmark applications and some real applications show that the heuristic finds near-optimal solution in almost all cases in a very small fraction of the time required to achieve the optimal solution.

Energy efficient mapping and voltage islanding for regular NoC under design constraints

Computational energy consumption of the processing elements (PEs) of a NoC can be significantly reduced by scaling down their voltage levels. This creates clusters of adjacent PEs operating at the same voltage level, known as voltage islands. Excessive number of voltage islands is undesirable from the physical design perspective and due to the overhead of level shifter energy consumption between adjacent voltage islands. Considering these issues during mapping of the PEs to the NoC routers, can potentially lead to acceptable solutions with reduced overall energy consumption. In this paper, we formulate the mapping problem as an optimisation problem. We present both optimal solution, obtained by solving a mixed integer linear program (MILP), and heuristic solution based on random greedy selection. Experimental results using benchmark and real applications show that the heuristic finds near-optimal solution in almost all cases in a very small fraction of the time required to achieve the optimal solution.

Impact of region-based faults on the connectivity of wireless networks

The traditional studies on fault-tolerance in networks assume that the faults are random in nature, i.e., the probability of a node failing is independent of its location in the deployment area. However, this assumption is no longer valid if the faults are spatially correlated. In this paper we focus on the study of the impact of region-based faults on wireless networks. Most of the studies on connectivity of wireless networks assume a unit disk graph model, i.e., links exist between two nodes if they are within a circular transmission range of one another. However, the unit disk graph model does not capture wireless communication environment accurately. The log-normal shadow fading model for communication was introduced to overcome the limitations of the unit disk graph model. In this paper we investigate connectivity issues of wireless networks in a log-normal shadow fading environment where the faults are spatially correlated. If d_min(G) denotes the minimum node degree of the network, we provide the analytical expression and method for computing P(d_min(G) >= 1) in a region-based fault scenario, where P(d_min(G) >= 1) denotes the probability of the minimum node degree being at least 1. Through extensive simulation, we find P(kG) >= 1), where k(G) represents the connectivity of the graph G formed by the distribution of nodes on a 2D plane and examine the relationship between P(d_min(G) >= 1) and P(k(G) >= 1).

On connectivity of Airborne Networks in presence of region-based faults

The U.S. Air Force is currently in the process of building an Airborne Network (AN), where the nodes are a set of heterogeneous, highly mobile, Airborne Networking Platforms (ANPs) - such as satellites, airplanes and unmanned aerial vehicles. Mobility pattern of nodes in a mobile network has significant impact on the coverage and connectivity properties of the network. The level of reliability needed for continuous operation of an AN may be difficult to achieve through a completely infrastructure-less mobile ad hoc networks. In an earlier paper, we proposed an architecture for an AN where a set of ANPs form the backbone of the AN. In this architecture, the ANPs may be viewed as mobile base stations with predictable and well-structured flight paths and the combat aircrafts on a mission as mobile clients. In this paper we consider the AN scenario where a part of the network might not be operational due to enemy attack and/or jamming. We consider faults that are spatially correlated (or region-based), that is faults due to an enemy attack are confined to a region. The goal is to design a robust AN so that no matter which region in the deployment area fails and at what time, the surviving nodes of the network will remain connected and be able to communicate with each other. We propose an algorithm that finds the minimum transmission range necessary to ensure network connectivity irrespective of location of the fault region and the time of the failure.

Approximation Algorithm for Avoiding Hotspot Formation of Sensor Networks for Temperature Sensitive Environments

Sensing and transmission phenomena of an implanted sensor dissipates energy which results in rise in temperature of its surroundings. Simultaneous operation of such multiple active sensors increases the temperature of the surrounding environment causing hotspots. Such hotspots are highly undesirable as they may cause damage to the environment as well as to the sensor network, posing a challenge for deployment of sensors. The problem is further enhanced for a temperature sensitive environment, as the allowable threshold temperature for such environments is less. Here we investigate the formation of hotspots in such temperature sensitive environments due to the heat dissipation of multiple active sensors and try to achieve a maximum coverage of such networks avoiding hotspots. We formulate this as a variation of the maximum independent set problem for hypergraphs. We devise an Integer Linear Program to achieve the optimal solution for the problem. We also provide a greedy heuristic solution for the problem. For a special case of this problem, where the hotspots are formed due to pairs of sensors only, we prove a 5-approximation bound for the greedy solution. Experimental results show that our algorithm achieves near-optimal solutions in almost all the test cases.

A unified approach for Multiple Multicast Tree Construction and Max-Min Fair rate allocation

Multicast communication is an efficient method of data transmission and distribution among a group, especially when network resources are inadequate and needs to be shared. Fair share of network resources, such as, bandwidth, is desirable in such cases. Although there has been an intensive research effort to design protocols and construct multicast routing graphs for a single multicast group, construction of multiple multicast groups and the fair allocation of network resources remains virtually unexplored. In this paper, a unified approach for the Multiple Multicast Tree Construction and Rate Allocation (MMTCRA) problem is addressed. The MMTCRA problem has been defined as an optimization problem with an objective of finding a Max-Min Fair rate allocation among the multiple multicast groups that co-exist in the network subject to the link-capacity constraints. The problem is proved to be NP-Complete. A Mixed Integer Linear Program (MILP) is formulated to achieve the optimal solution for this problem. A heuristic is proposed to solve the MMTCRA problem in polynomial time. The quality of the heuristic is evaluated by comparing the solution with the optimal solution for several randomly generated networks. A metric for user satisfaction, USat, has been defined in the paper. Experimental results show that 81% solutions obtained from heuristic have optimal USat, 95% solutions obtained from heuristic have optimal minimum allocated rate and the standard deviation of solutions are within 10% of optimal solutions.

On connectivity of airborne networks with unpredictable flight path of aircrafts

Mobility pattern of nodes in an airborne mobile network has significant impact on the coverage and connectivity of the network. Although networks with infrastructure may be able to provide a higher level of reliability than networks without infrastructure, in a contested air space, where U.S. forces do not have complete dominance of the air space, such an infrastructure may be infeasible. Such an environment necessitates a creation of completely mobile ad-hoc network by a group of ANPs. Since the movement of an ANP in a contested airspace depends not only on its own intention, but also the action of its adversary, its movement may be completely unpredictable. However, even this mobile ad-hoc network of ANPs with completely unpredictable flight path, should retain some desirable network properties, e.g., the network should remain connected at all times. However, this property can only be achieved if the on board transceivers have sufficient transmission range to ensure a connected network for all times, in spite of completely unpredictable movement pattern of the ANPs. In this paper, we analyze the minimum transmission range necessary to keep the airborne mobile ad-hoc network connected at all times. Assuming a specific variation of random walk as the mobility pattern of the ANPs, we compute the critical transmission range (CTR) to keep the network connected. Since the CTR analysis is asymptotic in nature, we conduct extensive simulation to compute the CTR for a finite number of ANPs. Our analytical results converges with the simulation results as the number of ANPs increases.