Abhishek Sinha

A Linear State-Space Analysis of the Migration Model in an Island Biogeography System

Biogeography deals with the study of the distribution of biodiversity over space and time and has been well studied by naturists and biologists for over the last five decades. Recently, the theory of biogeography has been applied to solve difficult engineering optimization problems in the form of a nature-inspired metaheuristic, known as biogeography-based optimization (BBO) algorithm. In this correspondence paper, we present an in-depth analysis of the linear time-invariant (LTI) system model of immigration and emigration of organisms in an island biogeography system that forms the basis of BBO. We find the bound of the eigenvalues of the general LTI system matrix using the Perron-Frobenius theorem from linear algebra. Based on the bounds of the eigenvalues, we further investigate four important properties of the LTI biogeography system, including the system reasonability with probability distribution vectors, stability, convergence, and nature of the equilibrium state. Our analysis gives a better insight into the dynamics of migration in actual biogeography systems and also helps in the understanding of the search mechanism of BBO on multimodal fitness landscapes.

Identification and Characterization of a FYVE Domain from the Early Diverging Eukaryote Giardia lamblia

The morphology of the endomembrane system of Giardia lamblia appears to be significantly different from higher eukaryotes. Therefore, the molecular mechanisms controlling vesicular trafficking are also likely to be altered. Since FYVE domain is a known regulator of endosomal trafficking, the authors used BLAST search to identify FYVE domain(s) in G. lamblia. A 990 amino acid long putative FYVE domain-containing ORF was identified, which contains all the conserved sequence elements in the ligand binding pocket. Phylogenetic analysis reveals that this domain is significantly diverged. The authors have shown that the corresponding gene is expressed in G. lamblia trophozoites and cysts. In spite of this phylogenetic divergence, in vitro biochemical assay indicates that this domain preferentially binds to phosphatidylinositol 3-phosphate {PtdIns(3)P}and in vivo expression of the GFP-tagged G. lamblia FYVE domain in S. cerevisiae, displays its selective localization to PtdIns(3)P-enriched endosomes. This is the first study to characterize a PtdIns(3)P effector protein in this early-diverged eukaryote.

Throughput-optimal broadcast in wireless networks with dynamic topology

We consider the problem of throughput-optimal broadcasting in a time-varying wireless network with an underlying Directed Acyclic (DAG) topology. Known broadcast algorithms route packets along pre-computed spanning trees. In large wireless networks with time-varying connectivities, the optimal trees are difficult to compute and maintain. In this paper, we propose a new online throughput-optimal broadcast algorithm, which takes packet-by-packet scheduling and routing decisions, obviating the need for any global topological structures, such as spanning trees. Our algorithm utilizes certain queue-like system-state information for making transmission decisions and hence, may be thought of as a generalization of the well-known back-pressure policy, which makes point-to-point unicast transmission decisions based on the local queue-length information. Technically, the back-pressure algorithm is derived by greedily stabilizing the queues. However, because of packet-duplications, the work-conservation principle is violated, and an analogous queueing process is non-trivial to define in the broadcast setting. To address this fundamental issue, we identify certain state variables whose dynamics behave like virtual queues. By stochastically stabilizing these virtual queues, we devise a throughput-optimal broadcast policy. We also derive new characterizations of the broadcast capacity of time-varying wireless DAGs and propose efficient algorithms to compute the capacity either exactly or approximately under various assumptions.

Distributed load management algorithms in anycast-based CDNs

Anycast is an internet addressing protocol where multiple hosts share the same IP-address. A popular architecture for modern Content Distribution Networks (CDNs) for geo-replicated services consists of multiple layers of proxy nodes for service and co-located DNS-servers for load-balancing among different proxies. Both the proxies and the DNS-servers use anycast addressing, which offers simplicity of design and high availability of service at the cost of partial loss of routing control. Due to the very nature of anycast, redirection actions by a DNS-server also affects loads at nearby proxies in the network. This makes the problem of optimal distributed load management highly challenging. In this paper, we propose and evaluate an analytical framework to formulate and solve the load-management problem in this context. We consider two distinct algorithms. In the first half of the paper, we pose the load-management problem as a convex optimization problem. Following a Kelly-type dual decomposition technique, we propose a fully-distributed load-management algorithm by introducing FastControl packets. This algorithm utilizes the underlying anycast mechanism itself to enable effective coordination among the nodes, thus obviating the need for any external control channel. In the second half of the paper, we consider an alternative greedy load-management heuristic, currently in production in a major commercial CDN. We study its dynamical characteristics and analytically identify its operational and stability properties. Finally, we critically evaluate both the algorithms and explore their optimality-vs-complexity trade-off using trace-driven simulations.

Throughput-optimal broadcast on directed acyclic graphs

We study the problem of broadcasting packets in wireless networks. At each time slot, a network controller activates non-interfering links and forwards packets to all nodes at a common rate; the maximum rate is referred to as the broadcast capacity of the wireless network. Existing policies achieve the broadcast capacity by balancing traffic over a set of spanning trees, which are difficult to maintain in a large and time-varying wireless network. We propose a new dynamic algorithm that achieves the broadcast capacity when the underlying network topology is a directed acyclic graph (DAG). This algorithm utilizes local queue-length information, does not use any global topological structures such as spanning trees, and uses the idea of in-order packet delivery to all network nodes. Although the in-order packet delivery constraint leads to degraded throughput in cyclic graphs, we show that it is throughput optimal in DAGs and can be exploited to simplify the design and analysis of optimal algorithms. Our simulation results show that the proposed algorithm has superior delay performance as compared to tree-based approaches.

Throughput-Optimal Broadcast in Wireless Networks with Point-to-Multipoint Transmissions

We consider the problem of efficient packet dissemination in wireless networks with point-to-multi-point wireless broadcast channels. We propose a dynamic policy, which achieves the broadcast capacity of the network. This policy is obtained by first transforming the original multi-hop network into a precedence-relaxed virtual single-hop network and then finding an optimal broadcast policy for the relaxed network. The resulting policy is shown to be throughput-optimal for the original wireless network using a sample-path argument. We also prove the NP-completeness of the finite-horizon broadcast problem, which is in contrast with the polynomial time solvability of the problem with point-to-point channels. Illustrative simulation results demonstrate the efficacy of the proposed broadcast policy in achieving the full broadcast capacity with low delay.

Optimal control for generalized network-flow problems

We consider the problem of throughput-optimal packet dissemination, in the presence of an arbitrary mix of unicast, broadcast, multicast and anycast traffic, in a general wireless network. We propose an online dynamic policy, called Universal Max-Weight (UMW), which solves the above problem efficiently. To the best of our knowledge, UMW is the first throughput-optimal algorithm of such versatility in the context of generalized network flow problems. Conceptually, the UMW policy is derived by relaxing the precedence constraints associated with multi-hop routing, and then solving a min-cost routing and max-weight scheduling problem on a virtual network of queues. When specialized to the unicast setting, the UMW policy yields a throughput-optimal cycle-free routing and link scheduling policy. This is in contrast to the well-known throughput-optimal BackPressure (BP) policy which allows for packet cycling, resulting in excessive delay. Extensive simulation results show that the proposed policy incurs a substantially lower delay as compared to the BP policy. The proof of throughput-optimality of the UMW policy combines techniques from stochastic Lyapunov theory with a sample path argument from adversarial queueing theory and may be of independent theoretical interest.

Deploy-As-You-Go Wireless Relay Placement: An Optimal Sequential Decision Approach Using the Multi-Relay Channel Model

We use information theoretic achievable rate formulas for the multi-relay channel to study the problem of as-you-go deployment of relay nodes. The achievable rate formulas are for full-duplex radios at the relays and for decode-and-forward relaying. Deployment is done along the straight line joining a source node and a sink node at an unknown distance from the source. The problem is for a deployment agent to walk from the source to the sink, deploying relays as he walks, given the knowledge of the wireless path-loss model, and given that the distance to the sink node is exponentially distributed with known mean. As a precursor to the formulation of the deploy-as-you-go problem, we apply the multi-relay channel achievable rate formula to obtain the optimal power allocation to relays placed along a line, at fixed locations. This permits us to obtain the optimal placement of a given number of nodes when the distance between the source and sink is given. Numerical work for the fixed source-sink distance case suggests that, at low attenuation, the relays are mostly clustered close to the source in order to be able to cooperate among themselves, whereas at high attenuation they are uniformly placed and work as repeaters. We also prove that the effect of path-loss can be entirely mitigated if a large enough number of relays are placed uniformly between the source and the sink. The structure of the optimal power allocation for a given placement of the nodes, then motivates us to formulate the problem of as-you-go placement of relays along a line of exponentially distributed length, and with the exponential path-loss model, so as to minimize a cost function that is additive over hops. The hop cost trades off a capacity limiting term, motivated from the optimal power allocation solution, against the cost of adding a relay node. We formulate the problem as a total cost Markov decision process, establish results for the value function, and provide insights into the placement policy and the performance of the deployed network via numerical exploration.

Distributed load management in anycast-based CDNs

Anycast is an internet addressing protocol where multiple hosts share the same IP-address. A popular architecture for modern Content Distribution Networks (CDNs) for geo-replicated HTTP-services consists of multiple layers of proxy nodes for service and co-located DNS-servers for load-balancing on different proxies. Both the proxies and the DNS-servers use anycast addressing, which offers simplicity of design and high availability of service at the cost of partial loss of routing control. Due to the very nature of anycast, load-management actions by a co-located DNS-server also affects loads at nearby proxies in the network. This makes the problem of distributed load management highly challenging. In this paper, we propose an analytical framework to formulate and solve the load-management problem in this context. We consider two distinct algorithms. In the first half of the paper, we pose the load-management problem as a convex optimization problem. Following a dual decomposition technique, we propose a fully-distributed load-management algorithm by introducing FastControl packets. This algorithm utilizes the underlying anycast mechanism itself to enable effective coordination among the nodes, thus obviating the need for any external control channel. In the second half of the paper, we consider an alternative greedy load-management heuristic, currently in production in a major commercial CDN. We study its dynamical characteristics and analytically identify its operational and stability properties. Finally, we critically evaluate both the algorithms and explore their optimality-vs-complexity trade-off using trace-driven simulations.

Throughput-Optimal Multi-Hop Broadcast Algorithms

We design throughput-optimal dynamic broadcast algorithms for multi-hop networks with arbitrary topologies. Most of the previous broadcast algorithms route packets along spanning trees. For large time-varying networks, computing and maintaining a set of spanning trees is not efficient, as the network-topology may change frequently. In this paper, we design a class of dynamic algorithms, which make simple packet-by-packet scheduling and routing decisions, and hence obviate the need for maintaining any global topological structures, such as spanning trees. Our algorithms may be conveniently understood as a non-trivial generalization of the familiar back-pressure algorithm for unicast traffic, which performs packet routing and scheduling based on queue lengths. However, in the broadcast setting, due to packet duplications, it is difficult to define appropriate queuing structures. We design and prove the optimality of a virtual queue-based algorithm, where virtual queues are defined for subsets of nodes. We then propose a multi-class broadcast policy, which combines the above scheduling algorithm with in-class-in-order packet forwarding, resulting in significant reduction in complexity. Finally, we evaluate the performance of the proposed algorithms via extensive numerical simulations.