arXiv subjects

Ke Liu

Publications and source records attributed to Ke Liu.

171 records · Page 10Linked to original sources

arXiv2009

Phase Transition on The Degree Sequence of a Mixed Random Graph Process

This paper focuses on the problem of the degree sequence for a mixed random graph process which continuously combines the {\it classical} model and the BA model. Note that the number of step added edges for the mixed model is random and non-uniformly bounded. By developing a comparing argument, phase transition on the degree distributions of the mixed model is revealed: while the {\it pure} classical model possesses a {\it exponential} degree sequence, the {\it pure} BA model and the mixed model possess {\it power law} degree sequences. As an application of the methodology, phase transition on the degree sequence of {\it another} mixed model with {\it hard copying} is also studied, especially, in the power law region, the inverse power can take any value greater than 1.

math.PR↗

arXiv2008

On the Degree Sequence and its Critical Phenomenon of an Evolving Random Graph Process

In this paper we focus on the problem of the degree sequence for the following random graph process. At any time-step $t$, one of the following three substeps is executed: with probability $α_1$, a new vertex $x_t$ and $m$ edges incident with $x_t$ are added; or, with probability $α-α_1$, $m$ edges are added; or finally, with probability $1-\a$, $m$ random edges are deleted. Note that in any case edges are added in the manner of preferential attachment. we prove that there exists a critical point $α_c$ satisfying: 1) if $α_1<α_c$, then the model has power law degree sequence; 2) if $α_1>α_c$, then the model has exponential degree sequence; and 3) if $α_1=α_c$, then the model has a degree sequence lying between the above two cases.

math.PR↗

arXiv2008

Stateless and Delivery Guaranteed Geometric Routing on Virtual Coordinate System

Stateless geographic routing provides relatively good performance at a fixed overhead, which is typically much lower than conventional routing protocols such as AODV. However, the performance of geographic routing is impacted by physical voids, and localization errors. Accordingly, virtual coordinate systems (VCS) were proposed as an alternative approach that is resilient to localization errors and that naturally routes around physical voids. However, VCS also faces virtual anomalies, causing their performance to trail geographic routing. In existing VCS routing protocols, there is a lack of an effective stateless and delivery guaranteed complementary routing algorithm that can be used to traverse voids. Most proposed solutions use variants of flooding or blind searching when a void is encountered. In this paper, we propose a spanning-path virtual coordinate system which can be used as a complete routing algorithm or as the complementary algorithm to greedy forwarding that is invoked when voids are encountered. With this approach, and for the first time, we demonstrate a stateless and delivery guaranteed geometric routing algorithm on VCS. When used in conjunction with our previously proposed aligned virtual coordinate system (AVCS), it out-performs not only all geometric routing protocols on VCS, but also geographic routing with accurate location information.

cs.NI↗

arXiv2006

The Aligned-Coordinated Geographical Routing for Multihop Wireless Networks

The stateless, low overhead and distributed nature of the Geographic routing protocols attract a lot of research attentions recently. Since the geographic routing would face void problems, leading to complementary routing such as perimeter routing which degrades the performance of geographic routing, most research works are focus on optimizing this complementary part of geographic routing to improve it. The greedy forwarding part of geographic routing provides an optimal routing performance in terms of path stretch. If the geographic routing could adapt the greedy forwarding more, its performance would be enhanced much more than to optimize the complementary routing such as perimeter routings. Our work is the first time to do so. The aligned physical coordinate is used to do the greedy forwarding routing decision which would lead more greedy forwarding. We evaluate our design to most geographic routing protocols, showing it helps much and maintain the stateless nature of geographic routing.

cs.NI↗

arXiv2006

JiTS: Just-in-Time Scheduling for Real-Time Sensor Data Dissemination

We consider the problem of real-time data dissemination in wireless sensor networks, in which data are associated with deadlines and it is desired for data to reach the sink(s) by their deadlines. To this end, existing real-time data dissemination work have developed packet scheduling schemes that prioritize packets according to their deadlines. In this paper, we first demonstrate that not only the scheduling discipline but also the routing protocol has a significant impact on the success of real-time sensor data dissemination. We show that the shortest path routing using the minimum number of hops leads to considerably better performance than Geographical Forwarding, which has often been used in existing real-time data dissemination work. We also observe that packet prioritization by itself is not enough for real-time data dissemination, since many high priority packets may simultaneously contend for network resources, deteriorating the network performance. Instead, real-time packets could be judiciously delayed to avoid severe contention as long as their deadlines can be met. Based on this observation, we propose a Just-in-Time Scheduling (JiTS) algorithm for scheduling data transmissions to alleviate the shortcomings of the existing solutions. We explore several policies for non-uniformly delaying data at different intermediate nodes to account for the higher expected contention as the packet gets closer to the sink(s). By an extensive simulation study, we demonstrate that JiTS can significantly improve the deadline miss ratio and packet drop ratio compared to existing approaches in various situations. Notably, JiTS improves the performance requiring neither lower layer support nor synchronization among the sensor nodes.

cs.NI↗

arXiv2006

Virtual Coordinate Backtracking for Void Traversal in Geographic Routing

Geographical routing protocols have several desirable features for use in ad hoc and sensor networks but are susceptible to voids and localization errors. Virtual coordinate systems are an alternative solution to geographically based routing protocols that works by overlaying a coordinate system on the sensors relative to well chosen reference points. VC is resilient to localization errors; however, we show that it is vulnerable to different forms of the void problem and have no viable complementary approach to overcome them. Specifically, we show that there are instances when packets reach nodes with no viable next hop nodes in the forwarding set. In addition, it is possible for nodes with the same coordinates to arise at different points in the network in the presence of voids. This paper identifies and analyzes these problems. It also compares several existing routing protocols based on Virtual Coordinate systems. Finally, it presents a new routing algorithm that uses backtracking to overcome voids to achieve high connectivity in the greedy phase, higher overall path quality and more resilience to localization errors. We show these properties using extensive simulation analysis.

cs.NI↗

arXiv2006

Aligned Virtual Coordinates for Greedy Routing in WSNs

Geographic routing provides relatively good performance at a much lower overhead than conventional routing protocols such as AODV. However, the performance of these protocols is impacted by physical voids, and localization errors. Accordingly, virtual coordinate systems (VCS) were proposed as an alternative approach that is resilient to localization errors and that naturally routes around physical voids. However, we show that VCS is vulnerable to different forms of the void problem and the performance of greedy routing on VCS is worse than that of geographic forwarding. We show that these anomalies are due to the integral nature of VCS, which causes quantization noise in the estimate of connectivity and node location. We propose an aligned virtual coordinate system (AVCS) on which the greedy routing success can be significantly improved. With our approach, and for the first time, we show that greedy routing on VCS out-performs that on physical coordinate systems even in the absence of localization errors. We compare AVCS against some of the most popular geographical routing protocols both on physical coordinate system and the virtual coordinate systems and show that AVCS significantly improves performance over the best known solutions.

cs.NI↗

arXiv2006

TARMAC: Traffic-Analysis Reslient MAC Protocol for Multi-Hop Wireless Networks

Traffic analysis in Multi-hop Wireless Networks can expose the structure of the network allowing attackers to focus their efforts on critical nodes. For example, jamming the only data sink in a sensor network can cripple the network. We propose a new communication protocol that is part of the MAC layer, but resides conceptually between the routing layer and MAC, that is resilient to traffic analysis. Each node broadcasts the data that it has to transmit according to a fixed transmission schedule that is independent of the traffic being generated, making the network immune to time correlation analysis. The transmission pattern is identical, with the exception of a possible time shift, at all nodes, removing spatial correlation of transmissions to network strucutre. Data for all neighbors resides in the same encrypted packet. Each neighbor then decides which subset of the data in a packet to forward onwards using a routing protocol whose details are orthogonal to the proposed scheme. We analyze the basic scheme, exploring the tradeoffs in terms of frequency of transmission and packet size. We also explore adaptive and time changing patterns and analyze their performance under a number of representative scenarios.

cs.NI↗

arXiv2005

The Three Node Wireless Network: Achievable Rates and Cooperation Strategies

We consider a wireless network composed of three nodes and limited by the half-duplex and total power constraints. This formulation encompasses many of the special cases studied in the literature and allows for capturing the common features shared by them. Here, we focus on three special cases, namely 1) Relay Channel, 2) Multicast Channel, and 3) Conference Channel. These special cases are judicially chosen to reflect varying degrees of complexity while highlighting the common ground shared by the different variants of the three node wireless network. For the relay channel, we propose a new cooperation scheme that exploits the wireless feedback gain. This scheme combines the benefits of decode-and-forward and compress-and-forward strategies and avoids the idealistic feedback assumption adopted in earlier works. Our analysis of the achievable rate of this scheme reveals the diminishing feedback gain at both the low and high signal-to-noise ratio regimes. Inspired by the proposed feedback strategy, we identify a greedy cooperation framework applicable to both the multicast and conference channels. Our performance analysis reveals several nice properties of the proposed greedy approach and the central role of cooperative source-channel coding in exploiting the receiver side information in the wireless network setting. Our proofs for the cooperative multicast with side-information rely on novel nested and independent binning encoders along with a list decoder.

cs.IT↗