Volume 4, Issue 1

We present a practical algorithm for multiplication of two sparse matrices. In fact if A and B are two matrices of size n with m 1 and m 2 non-zero elements respectively, then our algorithm performs O(min{m 1 n, m 2 n, m 1 m 2}) multiplications and O(k) additions where k is the number of non-zero elements in the tiny matrices that are obtained by the columns times rows matrix multiplication method. Note that in the useful case, k ≤ m 2 n. However, in Proposition 3.3 and Proposition 3.4 we obtain tight upper bounds for the complexity of additions. We also study the complexity of multiplication in a practical case where non-zero elements of A (resp. B) are distributed independently with uniform distribution among columns (resp. rows) of them and show that the expected number of multiplications is O(m 1 m 2/n). Finally a comparison of number of required multiplications in the naïve matrix multiplication, Strassen’s method and our algorithm is given.

OWL (Web Ontology Language) is the standard language for Semantic Web and is used in defining ontologies for Web. Temporal event data are ubiquitous in nature. Temporal data can be represented qualitatively using temporal relations in OWL, enabling temporal ordering of events which plays a vital role in task planners. The basic Allen’s temporal interval relations can be used to describe relations in OWL. Allen’s interval algebra is a well known formalism used to represent and reason the temporal knowledge. In this work, Allen’s interval algebra is extended by Reference Event based Temporal (REseT) relations to reduce the ambiguity in the before relation. The extended formalism is used in the representation of relations between time intervals and the viability of ordering of events in ontology is elucidated. This paper proposes a temporal knowledge representation and reasoning based event ordering system which helps in the temporal ordering of events. The advantage of this method is that it does not introduce any additional constructs in OWL and hence the existing reasoning tools and DL based query languages are capable of generating the linear order of events. The system is investigated experimentally using the COW (Correlates of War) dataset and has been evaluated using the Percent_ Similarity measure.

This paper proposes an adaptive online distributed solution for fault diagnosis in wireless sensor networks (WSNs). Fault diagnosis is achieved by comparing the heartbeat message generated by neighboring nodes and dissemination of decision made at each node. Time redundancy is used to detect the intermittent faults since an intermittent fault will not occur consistently. The diagnosis performance degradation due to intermittent faults in sensing and transient faults in communication is analyzed. A near optimal trade-off between detection latency and number of tests required to detect intermittent faults is obtained. Simulation results are provided and they show that this work performs better, from both time and energy complexity viewpoint.