arXiv subjects

Usman Ali

Publications and source records attributed to Usman Ali.

47 records · Page 3Linked to original sources

arXiv2016

On the Distinguishing number of Functigraphs

Let $G_{1}$ and $G_{2}$ be disjoint copies of a graph $G$, and let $g:V(G_{1})\rightarrow V(G_{2})$ be a function. A functigraph $F_{G}$ consists of the vertex set $V(G_{1})\cup V(G_{2})$ and the edge set $E(G_{1})\cup E(G_{2})\cup \{uv:g(u)=v\}$. In this paper, we extend the study of the distinguishing number of a graph to its functigraph. We discuss the behavior of the distinguishing number in passing from $G$ to $F_{G}$ and find its sharp lower and upper bounds. We also discuss the distinguishing number of functigraphs of complete graphs and join graphs.

math.CO↗

arXiv2016

Power Graph and Exchange Property for Resolving Sets

A formula for computing the metric dimension of a simple graph, having no singleton twin, is given. A sufficient condition for a simple graph to have the exchange property, for resolving sets, is found. Some families of power graphs of finite groups, having this exchange property, are identified. The metric dimension of the power graph of a dihedral group is also computed.

math.CO↗

arXiv2016

On Resolvability of a Graph Associated to a Finite Vector Space

The metric dimension of non-component graph, associated to a finite vector space, is determined. It is proved that the exchange property holds for resolving sets of the graph, except a special case. Some results are also related to an intersection graph.

math.CO↗

arXiv2016

Motion and Communication Co-optimization with Path Planning and Online Channel Estimation

This paper considers the problem of optimally balancing motion energy and communication transmission energy of a mobile robot tasked with transmitting a given number of data bits to a remote station, while navigating to a prespecified destination in a given amount of time. The problem is cast in the setting of optimal control, where the robot has to choose its path, acceleration, and transmission rate along the path so as to minimize its energy required for transmission and motion, while satisfying various power and communication constraints. We use realistic models for the robot's channel estimation, motion dynamics, and power and energy costs. The main contribution of the paper is to show how to co-optimize robot's path along with other communication and motion variables. Two versions of the problem are solved: the first is defined offline by assuming that all the channel measurements are taken before the robots starts moving, while in the second the channel estimation is updated while the robot is in motion, and hence it is solved online. In both cases we utilize an in-house algorithm that computes near-optimal solutions in little time, which enables its use in the online setting. The optimization strategy is described in detail and validated by simulation of realistic scenarios.

math.OC↗

arXiv2015

On the Efficacy of Live DDoS Detection with Hadoop

Distributed Denial of Service flooding attacks are one of the biggest challenges to the availability of online services today. These DDoS attacks overwhelm the victim with huge volume of traffic and render it incapable of performing normal communication or crashes it completely. If there are delays in detecting the flooding attacks, nothing much can be done except to manually disconnect the victim and fix the problem. With the rapid increase of DDoS volume and frequency, the current DDoS detection technologies are challenged to deal with huge attack volume in reasonable and affordable response time. In this paper, we propose HADEC, a Hadoop based Live DDoS Detection framework to tackle efficient analysis of flooding attacks by harnessing MapReduce and HDFS. We implemented a counter-based DDoS detection algorithm for four major flooding attacks (TCP-SYN, HTTP GET, UDP and ICMP) in MapReduce, consisting of map and reduce functions. We deployed a testbed to evaluate the performance of HADEC framework for live DDoS detection. Based on the experiments we showed that HADEC is capable of processing and detecting DDoS attacks in affordable time.

cs.CR↗

arXiv2014

Locating-Dominating sets in Hypergraphs

A hypergraph is a generalization of a graph where edges can connect any number of vertices. In this paper, we extend the study of locating-dominating sets to hypergraphs. Along with some basic results, sharp bounds for the location-domination number of hypergraphs in general and exact values with specified conditions are investigated. Moreover, locating-dominating sets in some specific hypergraphs are found.

math.CO↗

arXiv2013

Relative Garside elements of Artin monoids

We introduce a relative Garside element, the quotient of the corresponding Garside elements G1 and G2, for a pair of Artin monoids associated to Coxeter graphs Gamma1 and Gamma2, the second graph containing a new vertex. These relative elements give a recurrence relation between Garside elements. As an application, we compute explicitly the Garside elements of Artin monoids corresponding to spherical Coxeter graphs or the longest elements of the associated finite Coxeter groups.

math.GR↗

arXiv2011

Centralizer of Braids and Fibonacci Numbers

The paper encloses computation of simple centralizer of simple braids and their connection with Fibonacci numbers. Planarity of some commuting graphs is also discussed in the last section.

math.GR↗

arXiv2011

Minimizing the Number of Tiles in a Tiled Rectangle

In this paper, we prove that if a finite number of rectangles, every of which has at least one integer side, perfectly tile a big rectangle then there exists a strategy which reduces the number of these tiles (rectangles) without violating the condition on the borders of the tiles. Consequently this strategy leads to yet another solution to the famous rectangle tiling theorem.

math.HO↗

arXiv2011

Sliding Trellis-Based Frame Synchronization

Frame Synchronization (FS) is required in several communication standards in order to recover the individual frames that have been aggregated in a burst. This paper proposes a low-delay and reducedcomplexity Sliding Trellis (ST)-based FS technique, compared to our previously proposed trellis-based FS method. Each burst is divided into overlapping windows in which FS is performed. Useful information is propagated from one window to the next. The proposed method makes use of soft information provided by the channel, but also of all sources of redundancy present in the protocol stack. An illustration of our STbased approach for the WiMAX Media Access Control (MAC) layer is provided. When FS is performed on bursts transmitted over Rayleigh fading channel, the ST-based approach reduces the FS latency and complexity at the cost of a very small performance degradation compared to our full complexity trellis-based FS and outperforms state-of-the-art FS techniques.

cs.NI↗

arXiv2008

Conjugacy Classes of 3-Braid Group B_3

In this article we describe the summit sets in B_3, the smallest element in a summit set and we compute the Hilbert series corresponding to conjugacy classes.The results will be related to Birman-Menesco classification of knots with braid index three or less than three.

math.GT↗