Single-source Single-destination Research Articles

Enhancing Privacy in Graph Algorithms: Data-Oblivious Approaches to DFS and Dijkstra's Algorithm

Data obliviousness is characterized by a consistent sequence of operations irrespective of input data and data-independent memory accesses, making it a suitable solution for users utilizing outsourced storage data services who aim to conceal their data access patterns. In ACM SIGSAC 2013, data-oblivious algorithms were introduced for breadth-first search, single-source single-destination (SSSD) algorithms, maximum flow, and minimum spanning tree. In this study, we present novel data-oblivious algorithms designed for depth-first search and single-source shortest path (Dijkstra’s algorithm). Our proposed data-oblivious algorithms demonstrate efficiency comparable to non-data-oblivious counterparts, particularly for graphs containing fewer than 1000 nodes. This research contributes to advancing data privacy in outsourced storage services by providing effective data-oblivious solutions for common graph algorithms.

Stability and average delay in delay tolerant networks with Poisson packet arrivals and buffered relay nodes

We consider a single-source single-destination delay tolerant network (DTN) with Poisson packet arrivals. The source uses a store and forward protocol which makes multiple copies of a packet to relays which buffer them until delivery to the destination. We characterize the stability threshold, defined as the maximum value of arrival rate for which the source has finite average queue length, as a function of number of relays, relay contact rate, relay packet buffer capacity, and number of packet copies. We analyse DTNs without packet delivery feedback and with instantaneous feedback. For DTNs without packet delivery feedback, we obtain a non-asymptotic analytical stability threshold and show that it only doubles as the relay-buffer capacity increases from one to infinity. For DTNs with instantaneous packet delivery feedback, we characterize the stability threshold using simulations. We also present an analytical approximation for the stability threshold in the case of unit relay-buffer capacity, and show that it is approximately double of that without feedback for large number of packet copies and relays. For DTNs with and without feedback, we also study the average delay performance through simulations. We obtain analytical approximations for the average delays of the packets for DTNs without feedback. We observe that the last-in-first-out relay to destination packet transmission policy has the minimum delay.

A novel quantum algorithm for ant colony optimisation

Ant colony optimisation (ACO) is a commonly used meta-heuristic to solve complex combinatorial optimisation problems like the travelling salesman problem (TSP), vehicle routing problem (VRP) etc. However, classical ACO algorithms provide better optimal solutions but do not reduce computation time overhead to a significant extent. Algorithmic speed-up can be achieved by using parallelism offered by quantum computing. Existing quantum algorithms to solve ACO are either quantum-inspired classical algorithms or hybrid quantum-classical algorithms. Since all these algorithms need the intervention of classical computing, leveraging the true potential of quantum computing on real quantum hardware remains a challenge. This study's main contribution is to propose a fully quantum algorithm to solve ACO, enhancing the quantum information processing toolbox in the fault-tolerant quantum computing (FTQC) era. We have solved the single source single destination (SSSD) shortest-path problem using our proposed adaptive quantum circuit for representing the dynamic pheromone-updating strategy in real IBMQ devices. Our quantum ACO technique can be further used as a quantum ORACLE to solve complex optimisation problems in a fully quantum setup with significant speed up upon the availability of more qubits.

Planning the Shortest Path in Cluttered Environments: A Review and a Planar Convex Hull-Based Approach

AbstractRouting or path-planning is the problem of finding a collision-free and preferably shortest path in an environment usually scattered with polygonal or polyhedral obstacles. The geometric algorithms oftentimes tackle the problem by modeling the environment as a collision-free graph. Search algorithms such as Dijkstra’s can then be applied to find an optimal path on the created graph. Previously developed methods to construct the collision-free graph, without loss of generality, explore the entire workspace of the problem. For the single-source single-destination planning problems, this results in generating some unnecessary information that has little value and could increase the time complexity of the algorithm. In this paper, first a comprehensive review of the previous studies on the path-planning subject is presented. Next, an approach to address the planar problem based on the notion of convex hulls is introduced and its efficiency is tested on sample planar problems. The proposed algorithm focuses only on a portion of the workspace interacting with the straight line connecting the start and goal points. Hence, we are able to reduce the size of the roadmap while generating the exact globally optimal solution. Considering the worst case that all the obstacles in a planar workspace are intersecting, the algorithm yields a time complexity of O(n log(n/f)), with n being the total number of vertices and f being the number of obstacles. The computational complexity of the algorithm outperforms the previous attempts in reducing the size of the graph yet generates the exact solution.

Routing in Accumulative Multi-Hop Networks

This paper investigates the problem of finding optimal paths in single-source single-destination accumulative multi-hop networks. We consider a single source that communicates to a single destination assisted by several relays through multiple hops. At each hop, only one node transmits, while all the other nodes receive the transmitted signal, and store it after processing/decoding and mixing it with the signals received in previous hops. That is, we consider that terminals make use of advanced energy accumulation transmission/reception techniques, such as maximal ratio combining reception of repetition codes, or information accumulation with rateless codes. Accumulative techniques increase communication reliability, reduce energy consumption, and decrease latency. We investigate the properties that a routing metric must satisfy in these accumulative networks to guarantee that optimal paths can be computed with Dijkstra’s algorithm. We model the problem of routing in accumulative multi-hop networks, as the problem of routing in a hypergraph. We show that optimality properties in a traditional multi-hop network (monotonicity and isotonicity) are no longer useful and derive a new set of sufficient conditions for optimality. We illustrate these results by studying the minimum energy routing problem in static accumulative multi-hop networks for different forwarding strategies at relays.

Deadline-Aware Opportunistic Network Coding for Multi-Relay-Aided Single-Source Single-Destination Network

An opportunistic network coding (NC) scheme is proposed for the multi-relay-aided single-source single-destination network with transmission deadline. With the help of matrix analysis, the lower bound of decoding failure probability of the proposed scheme is given. Simulation results show that: 1) the proposed scheme outperforms NC based on direct recoding scheme and the lower bound is tight when the source-to-relay channel erasure probability is relatively small and 2) given fixed network parameters, the optimal number of systematic packets delivered within deadline could be determined by using the derived bound for maximizing the throughput.

A Near BER-Optimal Decoding Algorithm for Convolutionally Coded Relay Channels With the Decode-and-Forward Protocol

Relay-assisted communication has been shown to be an effective technique to improve the reliability and throughput of real-world wireless communication networks. It enables single-antenna users to form a virtual antenna array without installing multiple antennas at the transmitter or the receiver. This paper re-examines the decoding problem in the convolutionally coded relay channel with the classical decode-and-forward protocol. By tackling the challenge of modeling the error propagation effect at the relay, a near BER-optimal decoding (NBOD) algorithm at the destination is derived, assuming the availability of perfect receiver channel state information. Its decoding complexity is linear in the information block length, while the exact BER-optimal decoding algorithm with a sub-exponential complexity is still unknown. The major approximation involved in the derivation of the NBOD algorithm is the pairwise error probability approximation that causes a practically insignificant degradation from the optimal BER performance. Our simulation result confirms that the proposed NBOD algorithm can perform close to the maximum likelihood performance bound on BER in the three-node one-way relay channel scenario. In addition, we have further extended the proposed algorithm for more general single-source single-destination decode-and-forward-based relay networks. Simulation results further verify that the proposed NBOD algorithm can outperform existing decoding algorithms based on maximal-ratio combining and selective decode-and-forward in various relay channel scenarios at the cost of higher complexity.

A new time-dependent shortest path algorithm for multimodal transportation network

Abstract: The shortest path problem is a classical combinatorial optimization problem with countless real-life applications. Numerous algorithms have been proposed to solve the SPP since the classical Dijkstra algorithm, as well as new approaches to improve the algorithms’ optimality. But according to the real-world transport conditions, researchers began to study variants of this problem which include the time-dependent SPP and the multimodal networks. In this paper, we introduce our new time-dependent shortest path algorithm for multimodal transportation network. The proposed algorithm is a goal-oriented single-source single-destination algorithm. It takes into account the concept of “closeness” to the target node as heuristic to drive the search towards its destination. The optimality of the algorithm is principally based on computing a virtual path which is basically an Euclidean distance from the source to the target aiming at a restriction of the search space.

Efficient Capacity Computation and Power Optimization for Relay Networks

The capacity or approximations to capacity of various single-source single-destination relay network models has been characterized in terms of the cut-set upper bound. In principle, a direct computation of this bound requires evaluating the cut capacity over exponentially many cuts. We show that the minimum cut capacity of a relay network under some special assumptions can be cast as a minimization of a submodular function, and as a result, can be computed efficiently. We use this result to show that the capacity, or an approximation to the capacity within a constant gap for the Gaussian, wireless erasure, and Avestimehr-Diggavi-Tse deterministic relay network models can be computed in polynomial time. We present some empirical results showing that computing constant-gap approximations to the capacity of Gaussian relay networks with around 300 nodes can be done in order of minutes. For Gaussian networks, cut-set capacities are also functions of the powers assigned to the nodes. We consider a family of power optimization problems and show that they can be solved in a polynomial time. In particular, we show that the minimization of the sum of powers assigned to the nodes subject to a minimum rate constraint (measured in terms of cut-set bounds) can be computed in the polynomial time. We propose a heuristic algorithm to solve this problem and measure its performance through simulations on random Gaussian networks. We observe that in the optimal allocations, most of the power is assigned to a small subset of relays, which suggests that network simplification may be possible without excessive performance degradation.

Cross Layer AMC Scheduling for a Cooperative Wireless Communication System over Nakagami-m Fading Channels

We study a single-source single-destination cooperative wireless communication system with multiple relays operating in a modified decode-and-forward mode. Nakagami-m fading with additive white Gaussian noise is assumed for all inter-node channels. The bursty data packet arrival is modeled by a Markov-modulated Poisson process (MMPP). A packet feedback model is proposed to characterize packet loss in the wireless channel. An approximation to the steady state distribution of the proposed generalized discrete time M/G/1-type queue at the source is obtained by state truncation. Packet level performance of four transmission modes adopting different modulation and coding schemes is analyzed under a variety of channel and traffic conditions using the truncated queueing analysis. The network power is used as a criterion to find boundary curves of adaptive modulation and coding (AMC) scheduling for the cooperative wireless system. Two source node transmission protocols, namely the transmit-every-clock-tick (TREC) and the LAZY protocols, are examined for both the AMC scheduling and channel utilization analysis.

A Simple Recruitment Scheme of Multiple Nodes for Cooperative MAC

Physical (PHY) layer cooperation in a wireless network allows neighboring nodes to share their communication resources in order to create a virtual antenna array by means of distributed transmission and signal processing. A novel medium access control (MAC) protocol, called CoopMAC, has been recently proposed to integrate cooperation at the PHY layer with the MAC sublayer, thereby achieving substantial throughput and delay performance improvements. CoopMAC capitalizes on the broadcast nature of the wireless channel and rate adaptation, recruiting a single relay on the fly to support the communication of a particular source-destination pair. In this paper, we propose a cross-layer rate-adaptive design that opportunistically combines the recruitment of multiple cooperative nodes and carrier sensing multiple access with collision avoidance. We focus on a single-source single-destination setup, and develop a randomized cooperative framework, which is referred to as randomized CoopMAC (RCoopMAC). Thanks to the randomization of the coding rule, the RCoopMAC approach enables the blind participation of multiple relays at unison relying only on the mean channel state information (CSI) of the potential cooperating nodes, without introducing additional signaling overhead to coordinate the relaying process. The proposed RCoopMAC scheme is not only beneficial in substantially improving the link quality and therefore the sustainable data rates but, thanks to the decentralized and agnostic coding rule, it also allows to effectively recruit multiple relays in a robust fashion, i.e., even when the required mean CSI is partially outdated.

Efficient Tool for the Scheduling of Multiproduct Pipelines and Terminal Operations

This paper addresses the problem of scheduling a transmission pipeline carrying several petroleum products from a single oil refinery to a unique distribution center over a monthly horizon. The proposed approach is based on a very efficient mixed-integer linear programming (MILP) continuous-time formulation that is capable of determining the optimal pipeline batch sequence and lot sizes as well as the schedule of lot injections in the line and the timing of product deliveries to the distribution terminal. Moreover, the MILP model rigorously accounts for customer product demands on a daily basis, key terminal operations like lot settling periods for quality control tasks, and a predefined set of alternative lot sizes to get better control of tank availability. The approach also does not require the division of pipeline segments into a number of single-product packs of known capacities since the volume scale is also handled in a continuous manner. Results found for several examples involving the schedule of a real-world single-source single-destination multiproduct pipeline under different operational scenarios show that the proposed method leads to better pipeline schedules than previous approaches in a more rigorous way and at much lower computational cost.

A Dynamic Space-Time Network Flow Model for City Traffic Congestion

A space-time network is developed that represents traffic flows over time for a capacitated road transportation system having one-way and two-way streets. Traffic signal lights are explicitly incorporated into the network structure so that total travel time is a piecewise linear convex function of the number of units traveling on the streets. Hence congestion effects are explicitly considered while maintaining the linear nature of the model. The first example presented has one source and one sink. There is a unimodal buildup of traffic at the source (say a factory) which enters the street network as quickly as its capacity permits and proceeds through the network, stopping at red lights when necessary, toward the sink (a residential area). Two efficient solution methods are used: a network flow solution suitable for a multiple-source single-destination network, and a shortest path solution suitable only for a single-source single-destination network. Computations show that the arrival rate has multiple peaks which are induced by the stop lights. The second example has multiple sources and one sink and gives similar results, except that the arrival rate has a single board peak which is due to the extreme symmetry of the constraints of the problem.