Tech Reports in Computer Science and Engineering

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A Dual intepretation of Standard Constraints in Parametric Scheduling
(2000-03-07) Subramani, K.; Agrawala, A.
The problem of parametric scheduling in hard real-time systems, ( in the presence of linear relative constraints between the start and execution times of tasks ) was posed in the litreature. In an earlier paper, a polynomial time algorithm is presented for the case when the constraints are restricted to be standard ( defined in paper ) and the execution time vectors belong to an axis-parallel hyper-rectangle. In this paper, we extend their results in two directions. We first present a polynomial time algorithm for the case when the execution time vectors belong to arbitrary convex domains. We then show that the set of standard constraints can be extended to include arbitrary network constraints. Our insights into the problem occur primarily as a result of studying the dual polytope of the constraint system. (Also cross-refernced as UMIACS-TR-2000-11)
The Overlapped K-hop (OK) Clustering Algorithm
(2006-02-09T17:16:41Z) Youssef, Adel; Youssef, Moustafa; Younis, Mohamed; Agrawala, A.
Clustering is a standard approach for achieving efficient and scalable performance in wireless sensor networks. Clustering algorithms are mostly heuristic in nature and aim at generating the minimum number of disjoint clusters. In this report, we formulate the overlapping multi-hop clustering problem as an extension to the k-dominating set problem. Then we propose a fast, randomized, distributed multi-hop clustering algorithm (OK) for organizing the sensors in a wireless sensor network into overlapping clusters with the goal of minimizing the overall communication overhead, and processing complexity. OK assumes a quasi-stationary network where nodes are location-unaware and have equal significance. No synchronization is needed between nodes. OK is scalable; the clustering formation terminates in a constant time regardless of the network topology or size. The protocol incurs low overhead in terms of processing cycles and messages exchanged. We analyze the effect of different parameters (e.g. node density, network connectivity) on the performance of the clustering algorithm in terms of communication overhead, node coverage, and average cluster size. The results show that although we have overlapped clusters, the OK clustering algorithm still produces approximately equal-sized clusters.
The Parametric Polytope and its applications to a Scheduling Problem
(2000-03-23) Subrmani, K.; Agrawala, A.
An important feature in Real-time systems is {\em parameter impreciseness} i.e. the inability to accurately determine certain parameter values. The most common such parameter is {\em task execution time}. A second feature is the presence of complex relationships between tasks that constrain their execution. Traditional models do not accomodate either feature completely: (a) Variable execution times are modeled through a fixed value ( {\em worst-case} ), and (b) Relationships are limited to those that can be represented by precedence graphs. We present a task model that effectively captures {\em variable task execution time}, while simultaneously permitting arbitrary linear relationships between tasks. Our model finds applications in diverse areas such as real-time task scheduling, compiler scheduling, real-time database scheduling and machine control. This paper focuses primarily on the computational complexity of answering queries posed in our model; in particular we demonstrate the existence of constraint classes that make the scheduling problem {\em hard.} (Also cross-referenced as UMIACS-TR-2000-16)
The periodic polytope and its applications to a scheduling problem - A Static Perspective
(2000-05-09) Subramani, K.; Agrawala, A.
Parameter variability and the existence of complex constraints between tasks are assured features of real-time scheduling. {\em Periodicity} of task sets is an additional feature that needs to be accomodated. Traditional scheduling models ignore the complexities involved in real-time scheduling by making simplistic assumptions about task interactions. In this paper, we present a model that captures the issues that we deem central to real-time scheduling in periodic task sets and demonstrate the existence of efficient and easily implementable algorithms for addressing schedulability queries in this model. Our model is very general and applicable to diverse areas ranging from real-time process scheduling in operating systems and avionics to manufacturing and traffic control. (Also cross-referenced as UMIACS-TR-2000-25)
The Static Polytope and its applications to a scheduling problem
(2000-03-14) Subramani, K.; Agrawala, A.
In the design of real-time systems, it is often the case that certain process parameters ( such as {\em execution time} ) are not known precisely. The challenge in real-time system design is to develop techniques that efficiently meet the requirements of impreciseness. Traditional models tend to simplify the issue of impreciseness by assuming {\em worst-case} times. This assumption is unrealistic and at the same time, may cause certain constraints to be violated at run-time. In this paper, we shall study the problem of scheduling a set of ordered, non-preemptive processes under non-constant execution times. Typical applications for variable execution time scheduling include process scheduling in Real-time Operating Systems such as Maruti, compiler scheduling, database transaction scheduling and automated machine control. An important feature of application areas such as robotics is the interaction between execution times of various processes. We explicitly model this interaction through the representation of execution time vectors as points in convex sets. We present both sequential and parallel algorithms for determining the existence of a static schedule. (Also cross-referenced as UMIACS-TR-2000-14)