Mental health challenges continue to rise globally, yet access to effective and personalized support remains insufficient. While Large Language Models (LLMs) have shown its promise in this area, most existing solutions lack personalization, pose privacy risks, and often generate unreliable or generic responses. In this study, we present a novel approach that enhances LLM-based mental health support through fine-tuning on a combination of public and synthetically generated mental health datasets. We further propose a dynamic prompt strategy that extracts relevant mental health entities from patient conversations, such as symptoms and emotions, and retrieves relevant information from diverse data sources. We leverage function calling with Retrieval-Augmented Generation (RAG) to produce context-aware, personalized responses. Empirical comparisons with existing models demonstrate that our approach achieves higher accuracy and generates responses that are better aligned with individual user needs.

Artificial Intelligence-Generated Content, a subset of Generative Artificial Intelligence, holds significant potential for advancing the e-health sector by generating diverse forms of data. In this paper, we propose an end-to-end class-conditioned framework that addresses the challenge of data scarcity in health applications by generating synthetic medical images and text data, evaluating on practical applications such as retinopathy detection, skin infections and mental health assessments. Our framework integrates Diffusion and Large Language Models (LLMs) to generate data that closely match real-world patterns, which is essential for improving downstream task performance and model robustness in e-health applications. Experimental results demonstrate that the synthetic images produced by the proposed diffusion model outperform traditional GAN architectures. Similarly, in the text modality, data generated by the uncensored LLM achieves significantly better alignment with real-world data than censored models in replicating the authentic tone.

Large language models (LLMs) have demonstrated remarkable capabilities in code generation across various domains. However, their effectiveness in generating simulation scripts for domain-specific environments like ns-3 remains underexplored. Despite the growing interest in automating network simulations, existing tools primarily focus on interactive automation over rigorous evaluation. To facilitate systematic evaluation, we introduce SIMCODE, the first benchmark to evaluate LLMs’ ability to generate ns-3 simulation code from natural language. SIMCODE includes 400 tasks across introductory, intermediate, and advanced levels, with solutions and test cases. Using SIM-CODE, we evaluate three prominent LLMs, Gemini-2.0, GPT-4.1, and Qwen-3, across six prompt techniques. Furthermore, investigating task-specific fine-tuning’s impact reveals that while GPT-4.1 outperforms others, execution accuracy remains modest, with substantial room for improvement. Error analysis identifies missing headers and API mismatches as dominant failures. Nevertheless, SIMCODE provides a foundational step toward evaluating LLMs and research in domain-aware generative systems.

Hosting virtual network function (VNF) on the edge devices in modern IoT networks significantly reduces the number of appliance hardware needed. It also expedites significant routing and load-balancing processes and reduces power consumption and maintenance costs for an extensive network. Therefore, placing VNFs on edge devices with efficient resource utilization to serve the growing number of IoT devices is an important research question for the network community. This research proposes a many-to-many VNF placement model with fairness built in. One user (IoT device) can access multiple VNFs, and many VNFs can be hosted into a single host (edge device). We give an optimization model and valid inequalities for the optimal placement of VNFs to minimize the total latency. A branch and cut algorithm is also developed here for solving the model optimally. We evaluate the model with synthetic data for a many-to-many and one-to-one mapping of VNFs and hosts. A detailed simulation shows that the proposed algorithm(s) can produce an optimal and fair placement in near real-time on realistically sized instances.

Extreme Edge Computing (XEC) is a serverless edge computing paradigm where computational tasks are offloaded to and from extreme edge devices (XEDs). XEDs, a subset of IoT devices that consists of consumer-owned devices capable of offering computational resources. Being data-rich, XEDs can facilitate the training of more accurate Machine Learning (ML) models. However, their unpredictable computational behavior, which follows the consumers’ usage, and transient availability pose challenges that traditional Federated Learning (FL) approaches may struggle to address. To this end, we propose a new framework for decentralized FL in XEC systems designed to address the computational reliability of XEDs and optimize the computational resource allocation. Moreover, to encourage XEDs’ participation in the FL training process, we introduce an Auction-based incentive mechanism. This mechanism models the interactions between XEDs, considering both the computational characteristics and the data quality of XEDs. Furthermore, we present two solution approaches: an optimization approach and a heuristic approach, each introducing a complexity-performance trade-off. Finally, we evaluate and demonstrate the effectiveness of our proposed framework in improving the performance and reliability of XEDs in decentralized learning environments.

Metaverse can unleash the potentials of Internet of Sense (IoS) communication by intertwining objects and environment between physical world and parallel virtual world. In order to digitally experience smell or taste and navigate effortlessly in virtual reality, optimal resource allocation to strengthen sensing data based infrastructure system is a critical research challenge. The Metaverse Infrastructure Service Providers (MISPs) tap into data marketplace and subscribe to resources in advance for fulfilling the needs of data consumers and users. The demand of the data based services being uncertain, non-optimal subscription schemes may lead to unwanted resource wastage or shortage. Thus, we propose a Stochastic Integer Programming (SIP) model with two phase reservation and on-demand plans for optimal resource allocation in data marketplace. Further along this line, we strive to predict the demand by leveraging Quantum Neural Networks (QNN) that is able to learn with fewer historical data in comparison to classical machine/deep learning paradigms. Extensive simulation results justify that QNN as a supporting model can significantly reduce the computational complexities of SIP formulation. This research can contribute to reduce Metaverse resource fabrication costs, upgrade the profit margin for MISPs by increasing data based service sales revenue, provide real-time resource management decisions, and overall make real impacts in the virtual world.

Metaverse refers to the intersection of parallel virtual worlds with their physical counterparts by allowing users to interact with virtual people, objects, and environments. Resource allocation in various aspects of Metaverse domains, called as MetaSlices hereinafter, is a crucial optimization research problem. To serve this purpose, we consider a MetaSlice framework with the notion of sharing resources among common functions and enable placing time-sensitive services at the edge of multi-tier architecture in proximity to users. Unfortunately, the classical Integer Linear Programming is inappropriate for such heavily constrained optimization problem due to the extensive running time and memory. Hence, we model a novel Quadratic Unconstrained Binary Optimization (QUBO) formulation to simultaneously optimize resources and secure Quality of Service for MetaSlices as a paradigm shift towards quantum computing. Furthermore, we propose to employ a hybrid classical-quantum WSQA to optimize resource under uncertainty, offer ultra-low running time, and increase service acceptance rate/scalability in resource-hungry and dynamic Metaverse system. Extensive simulation results demonstrate that WSQA outperforms other classical and standalone quantum annealing approaches, even with the limited availability of qubits (quantum resources). Thus, this research paves the way to decrease massive resource fabrication costs and upgrade profit margin for Metaverse Internet Service Providers, while simultaneously providing real-time services for Metaverse users.

Metaverse can unleash the potentials of Internet of Sense (IoS) communication by intertwining objects and environment between physical world and parallel virtual world. In order to digitally experience smell or taste and navigate effortlessly in virtual reality, optimal resource allocation to strengthen sensing data based infrastructure system is a critical research challenge. The Metaverse Infrastructure Service Providers (MISPs) tap into data marketplace and subscribe to resources in advance for fulfilling the needs of data consumers and users. The demand of the data based services being uncertain, non-optimal subscription schemes may lead to unwanted resource wastage or shortage. Thus, we propose a Stochastic Integer Programming (SIP) model with two phase reservation and on-demand plans for optimal resource allocation in data marketplace. Further along this line, we strive to predict the demand by leveraging Quantum Neural Networks (QNN) that is able to learn with fewer historical data in comparison to classical machine/deep learning paradigms. Extensive simulation results justify that QNN as a supporting model can significantly reduce the computational complexities of SIP formulation. This research can contribute to reduce Metaverse resource fabrication costs, upgrade the profit margin for MISPs by increasing data based service sales revenue, provide real-time resource management decisions, and overall make real impacts in the virtual world.

Significant research has been done in the medical domain using machine learning and clinical data sets. Although there are many interesting and influential clinical research works in the fields of healthcare and health services using machine learning, there is a need to apply machine learning in the field of health human resource planning. This study uses physician billing data and machine learning to identify and classify family physicians with the goal of improving health human resource planning. This research is essential for policy makers because it is important to know the number of family physicians practicing in certain geographical regions for providing timely care. Additionally, this issue becomes particularly important when it comes to serving communities with fewer resources such as the rural areas of Northwestern Ontario, where family physicians need to work to their full scope of practice, provide more services than physicians working in urban areas, to meet the needs of patients. In this study, recursive feature elimination method is used to reduce the number of predictors for the classification problems. As the result of this process, the most important features include physician’s rurality, full-time equivalent hours, age, and years of experience. Further, several machine learning models are used to solve binary and multi-class classification problems. Gradient boosting machine learning was the most accurate in predicting family physician practice, with a receiver operating characteristic value, ROC value, of 0.73 and 0.72 for binary and multi-class classification, respectively.

The prospective Internet of Things (IoT) vertical use cases demand latency perception, privacy preservation, and scalability intelligence equipped Virtual Network Function (VNF) orchestration in a dynamic context. With the massive growth of IoT connectivity, smart VNF orchestration with real-time deployment abilities is vital for the ubiquitous digital network environment. Hence, this paper collaboratively considers all the future service orchestration specifications. Moreover, we urge the necessity to go beyond the traditional service deployment framework and introduce VNF allocation at edge cloudlet small scale data-centers. Extensive simulation results manifest the applicability and potential of our proposed deep learning models with the twist of ensemble techniques for automated VNF orchestration. Additionally, our proposed ensemble deep learning aided approach inspires the employment of intelligent orchestrator to address 6G network era challenges for perpetual telecommunication research enigmas.

Among the massive pool of Internet of Things (IoT) devices in network function virtualization (NFV) context, the urgency for efficient service orchestration is constantly growing. The emerging challenges can be addressed as collaborative optimization of resource utilities and ensuring Quality-of-Service (QoS) with prompt orchestration in dynamic, congested, and resource-hungry IoT networks. Traditional mathematical programming models are NP-hard, hence inappropriate for time sensitive IoT scenarios. This paper promotes the need to go beyond the realms and propose an intelligent Deep Q-Network (DQN) driven service function chain (SFC) orchestration, named as DSO hereafter. We further equip this proposed DSO model with the notion of sharing the flow of already deployed network function rather than urging a new instantiation. The sharing conceptualization improves resource utilization, and DQN is employed for adaptive, robust, and swift orchestration. Our extensive simulation results demonstrate the remarkable capability and adaptability of the proposed DSO model for cutting back running time (≈ 10 hours) and ensuring near-optimal resource utilization across extremely dense IoT substrate network settings. Thus, this research can be regarded as a pioneering tread to scale down massive IoT resource fabrication costs, upgrade profit margin for providers, and sustain QoS.

Recently, the problem of optimal resource scheduling for the increasingly growing number of smart vehicles has emerged as a daunting research challenge. While Over the Air (OTA) software updates are critical for the safe routing/driving of smart vehicles, they consume precious network resources if not planned or scheduled appropriately. In this paper, we consider a smart fog computing network to serve the smart vehicles with OTA updates and present two optimal resource scheduling problems SP1and SP2. The objective of SP1is to minimize the maximum waiting time of any smart vehicle and the objective of SP2aims to minimize the maximum transmission time of any channel. These problems cannot always ascertain optimal solutions in polynomial time. We first propose a random algorithm and a greedy algorithm for these problems and find that these two algorithms may not perform adequately in many cases. Hence, we propose a local search algorithm which takes any feasible solution of a scheduling problem as input and improves that solution. Computer-based simulations demonstrate the effectiveness of our proposed algorithms.

In the sixth generation (6G) networks, due to the massive Internet of Things (IoT) connectivity and substantial growth of communication traffic, an effective Virtual Network Function (VNF) orchestration scheme is anticipated to function dynamically and intelligently. Moving beyond the traditional paradigm of the VNF orchestration and employing VNFs on the network edge located cloudlets based on the inspiration from multi-access edge computing can intensify the overall performance of delay-sensitive applications. In this paper, we intend to investigate how to simultaneously leverage the ensembling of multiple deep learning models for proper calibration to provide real-time VNF placement solutions. We also address the challenges associated with state-of-the-art approaches to deal with dynamic network traffic and topology patterns. Our envisioned methods, based on Convolutional Neural Networks and Artificial Neural Networks named as E-ConvNets and E-ANN respectively, suggest two proactive VNF deployment strategies. These VNF placement strategies demonstrate (simulation results) encouraging performance (optimality gap nearly 7%) in terms of minimizing relocation and communication costs, and high scalability intelligence factor (around 0.93). Moreover, the presented results are further indications of integrating edge computing and deep learning-based strategies into similar research enigmas for future telecommunication networks.

In a mobile edge computing (MEC) network, mobile devices could selectively offload tasks to the edge server(s) to save time and energy. However, we should consider many dynamic factors in task offloading optimization, which increases the complexity of this problem. Instead of executing the traditional optimization algorithm repeatedly, a well-trained empirical model such as an artificial neural network could be more efficient in decision making. In this research, considering the potential uneven spatial distribution of mobile devices in an MEC network with multiple wireless edge gateways, we allow an edge gateway to offload tasks to a nearby edge gateway further. We propose a deep reinforcement learning-based joint optimization approach for both device-level and edge-level task offloading. Experimental results show that the proposed approach achieves a near-optimal task delay performance and a better trade-off between the task delay and the energy consumption on tasks.

On-demand resource management is a challenging prospect, especially in communication networks where the users' requirements of network resources are volatile. This challenge is magnified by the current shift of hardware-dependent network technologies into virtual Network Functions (vNFs) in a cloud-based platform and the proliferation of the Internet of Things (IoT) networks. vNFs are an integral part of edge devices that aims to improve service providers' response time, eliminate redundancy, and end to end latency results in operators' lower operating costs significantly. The efficiency of such a virtualized system largely depends on the optimization of resource allocation between users and Virtual Machines (VM) or hosting devices. One approach to addressed this issue is to minimize the latency of the entire communication network, however, the concern is that this mechanism does not ensure fairness of resource allocation because some of the users may receive enhanced services than others. In the previous study, a Stable Matching Algorithm is proposed to minimize the latency between vNFs and VMs but the algorithm failed to ensure the fairness of the requested services and server elements. In this study, we further extend the previous model to ensure the fairness. Our proposed solution minimizes the maximum latency in the network. This problem is an NP-hard and hence we provide a local search based solution. The experimental result shows improved fairness from other approaches and the fairness index is close to the optimal, which in fact represents the elimination of imbalances to a great extent.

This paper studies incentive-based peer-to-peer (P2P) energy trading between sellers and buyers in a smart grid distributed system. When designing an energy trading model the main goal is to maximize the social welfare of the involved parties. Peer-to-peer energy trading is a novel mechanism of power system operation which allows users to generate and trade renewable energy. Buyers are considered to be consumers and sellers are considered to be prosumers (producers and consumers of energy) with respect to time. Buyers are more motivated to purchase energy from the seller since the energy was generated from a green source and is typically cheaper than the main grid. Furthermore, by producing clean energy and distributing within small networks, the transmission line stress is mitigated since the overall demand required from the main grid is reduced. In this paper, we model the interaction as single-sided auction taking into consideration the grid infrastructure constraints (e.g capacity) and cost while maximizing the profit of the players. We assess through theoretical analysis and simulations the bidding properties including individually rational, truthful, computationally efficient, and fairness.

Radio Frequency Identification (RFID) plays a key role in the Internet of things (IoT). The type of scenario that needs to use many readers to cover a large area is a dense RFID environment scenario. In supply-chain management, companies such as Wal-Mart use dense RFID reader systems to track products [1]. Collisions usually happen in dense RFID reader systems, which reduce the number of tags that can be read by the system. Many algorithms were designed to eliminate the collisions in a dense RFID environment. A Maximum-Weight-Independent-Set-Based Algorithm (MWISBA) [2] is used to solve the dense RFID readers' arrangement uses a graph-based algorithm to get the MWIS. However, MWISBA does not consider interference range, it can only avoid reader-to-tag collisions. Based on MWISBA, an improved algorithm called MWISBAII [3] can avoid both reader-to-tag collisions and reader-to-reader collisions. However, both MWISBA and MWISBAII are centralized algorithms. In this paper, we propose a distributed realization of MWISBAII. In our distributed algorithm, each reader can communicate with other neighbor readers to share and collect information; making the local decision afterwards. The experimental results show that our distributed algorithm can get almost the same performance as the MWISBAII.

The Controller Placement Problem (CPP), in Software Defined Networks (SDNs), deals with placing an optimal number of controllers. The CPP aims to maximize the network throughput and minimize different latencies like flow-setup latency and route-synchronization latency. In recent years, many solutions to the CPP have been proposed- some approaches work with a single parameter like the average propagation delay of a network, reliability, load balancing, etc., while some other approaches provide exhaustive solutions which optimize multiple parameters. However, very few researches propose non-exhaustive solutions which simultaneously optimize more than one parameter. We propose a novel controller placement algorithm which clusters the SDNs in polynomial time complexity. Our proposed algorithm Degree-based Balanced Clustering (DBC) minimizes overall flow-setup latency as well as route-synchronization latency and balances the loads of the controllers at the same time. DBC divides a network into several clusters, places a controller in each cluster, and also selects an optimal number of controllers. Simulation results suggest that DBC outperforms existing state-of-the-art algorithms in terms of different latencies and also performs load balancing among the controllers.

Device-to-device (D2D) communication in an underlaying cellular network is becoming increasingly common in telecommunication systems, and it will play a vital role in the fifth generation (5G) and beyond. The base stations manage the cellular users. The D2D pairs communicate directly without using the base station. This direct and short-range communication of D2D pairs improve the energy efficiency. It also enables inter-device applications such as location-based emergency services, commercial advertisements, etc. D2D pairs share spectrum resources from cellular users. This sharing generates a significant amount of interference in mobile communication. We study the problem of assigning resources from cellular users to D2D pairs such that the total interference is minimized subject to a minimum target sum rate. We give a two-phase combinatorial algorithm which computes an allocation of resources subject to the sum rate constraint. For the case when the interference between any communicating D2D pair is uniform, the algorithm finds an optimal solution in polynomial time.

In a device to device (D2D) communication underlaying cellular network, total system sum rate can be improved if cellular user equipments (UEs) and D2D pairs share resource blocks (RBs). We consider such an optimization problem where the objective is to maximize the total sum rate of the system while sharing RBs among cellular UEs and D2D pairs and maintaining some quality of service (QoS) requirements. Most of the existing algorithms consider that sharing can only improve the sum rate. However, some sharing can also decrease the sum rate. Considering this observation, we design an optimal algorithm based on weighted bipartite matching which avoids such sharing and maximize the total system sum rate. We prove that our algorithm is optimal and validate the results through simulations which shows that our algorithm outperforms other existing heuristics in terms of maximizing system sum rate. Our algorithm also performs better in terms of total interference introduced through the sharing of resource blocks among cellular equipments and D2D pairs.

Interference minimization while maintaining a target system sum rate by sharing resources among cellular User Equipments (UEs) and Device-to-Device pairs (D2D) is an important research question in Long Term Evolution (LTE). We propose a two phase resource allocation algorithm for this research problem. In the first phase, we use the bipartite matching algorithm to minimize the interference which also avoids matching that can decrease the total system sum rate. In some cases, after the first phase, the solution may not be the optimal one. Therefore, in the second phase, we use a local search algorithm to improve the solution. We compare our algorithm with two other existing algorithms (MIKIRA and TAFIRA) which address the same research problem. We prove that MIKIRA fails to provide feasible solutions in most of the cases. We also show that the performance ratio of TAFIRA can be unbounded in the worst case. Moreover, in some cases, TAFIRA can not provide any solution of the problem where solutions exist. We prove that, our algorithm always provides the solution whenever it exists. We perform extensive simulations of the algorithms and find that in all cases, our solution is either optimal or very close to the optimal.

Interference coordination while sharing cellular radio resources with Device-to-Device (D2D) pairs needs to be done in the short LTE scheduling period of 1 ms. In this paper, we propose a fast, two-phase auction based, fair and interference aware resource allocation algorithm (TAFIRA) for underlaying D2D communication. TAFIRA can be used to minimize the interference both at the evolved Node B (eNB) and the receiver of the D2D pairs while simultaneously maintaining a target system sum rate and ensuring fair allocation of cellular resources among D2D pairs. We compare TAFIRA with a MInimum Knapsack based Interference Resource Allocation algorithm (MIKIRA) and a random allocation technique. The time complexity of TAFIRA on average is O(m2n), where m and n are the number of D2D pairs and number of cellular users respectively. Our simulation results how that, TAFIRA obtains a much better system sum rate while incurring very little increased interference at the eNB and the D2D receivers when compared with MIKIRA and the random approach. TAFIRA also shows much more fairness in allocating cellular resources among the D2D pairs when compared with MIKIRA.

Redundant readers elimination is one of the fundamental optimization research problems in RFID networks. The problem is NP-hard and can be solved approximately using best known centralized set cover algorithms. However, either distributed or localized solutions for this problem are much more realistic and useful in practice. Different distributed and a few local algorithms are known in the literature. In this paper, we propose a cellular automaton based local algorithm for the redundant readers elimination optimization problem. To the best of our knowledge, this is the first cellular automaton based algorithm (that is, a strictly local algorithm) to solve this problem. We compare the performance of our algorithm with other local algorithms and establish that our algorithm gives much better results. We also compare our algorithm with the best known centralized approximation algorithm and find very competitive results even though our algorithm is a local one.

Resource allocation for Device-to-Device (D2D) communication underlaying cellular network poses new challenges in terms of interference while at the same time provides increased system sum rate. In this paper, we propose a local search based resource allocation algorithm (LORA) for allocating resource blocks to D2D devices that are shared with Long Term Evolution (LTE) cellular users. We first formulate the problem of downlink resource block (RB) allocation to D2D users from cellular users as a computationally expensive mixed integer nonlinear programming (MINLP) problem. However, as the optimal solution of an MINLP can take exponential time to compute, we propose a local search based algorithm to compute a locally optimal solution based on an initial feasible solution. We compare the obtained system sum rate from this local search algorithm with a well-known greedy heuristic based resource allocation algorithm and a random resource allocation algorithm. The simulation results show that LORA achieves an overall better system sum rate compared to the other algorithms for RB allocation while maintaining the signal quality at the cellular users and the D2D receivers.

Object monitoring is an important application of mobile wireless sensor networks. Several algorithms appear in the literature for different variants of the object monitoring problem. Most of them are either centralized or distributed. Algorithms for mobile wireless sensor networks involve many aspects not dealt with in traditional networks and hence mobile wireless networks can be viewed as an unconventional computation model. We design algorithms for mobile wireless sensor networks based on another unconventional model of computation namely, the biologically inspired cellular automata. We design a cellular automaton based algorithm for an object monitoring problem where initially a number of mobile sensors and mobile objects are deployed randomly in a dense area of the network and they are allowed to move within the network. Our main goal is to monitor the mobile objects by the mobile sensors as long as possible. To the best of our knowledge, we propose the first cellular automaton based algorithm for this problem. We find that our algorithm can monitor a good number of objects constantly over time.

We propose a cellular automaton based local algorithm to reposition mobile sensors of a wireless sensors network. Our main goal is to maximize the total coverage of the network while maintaining the connectivity among the sensors. In most of the applications, it is not feasible to deploy mobile sensors using a global algorithm. Typically, the sensors are initially densely deployed and use their mobility to increase the coverage of the network. Our algorithm uses very limited local information to compute the final positions of the sensors. In many applications, maximizing the coverage is not the only objective; the sensors also need to communicate with each other. Therefore, maintaining connectivity when the sensors disperse is an important goal, and our algorithm achieves this as well. We perform different simulations on different starting configurations. For some configurations, the optimal solution is arrived at, while for others a near optimal solution is obtained.

We design new cellular automaton based algorithms to improve coverage in a network with mobile sensors. The algorithms can be useful in applications where sensors are initially deployed in one place and need to disperse to the environment autonomously, or in situations where in certain areas sensors may be destroyed (e.g. due to a natural disaster), and the sensors need to use their mobility in order to restore coverage. We propose a cellular automaton model that divides the neighborhood of a cell into four (North West, North East, South West and South East) quadrants and the sensors try to find out the directions where they can move to increase the coverage. We compared our model with a previous model for different initial configurations and have found that our model reaches a comparable coverage more quickly. Our algorithms use two parameter values to guide the movements of the sensors. Especially with the best choices of the parameter values, our algorithms require the sensors to make considerably fewer atomic movements than the earlier algorithm. For mobile sensor networks, energy consumption is largely determined by the amount of movement, and minimizing movement will increase the life time of the network.

We study the problem of computing an energy-efficient data delivery scheme in wireless sensor networks that leverages the knowledge of a set of trajectories of mobile sinks in the network to route data from the sensors to the mobile sinks. Sensors collect data from the environment and instead of directly sending them to the mobile sinks (henceforth simply “sinks”), they route data to a number of selected nodes (we call them relay or stashing nodes) in the network. These stashing nodes lie on the trajectories of the sinks, and relay the received data directly to the sinks on behalf of the sensors. Assuming a set of p different applications being executed on each sensor node, we consider the following problem: Given a set of p trajectories T1, T2, ..., TPcorresponding to p sinks, where sink Ti is dedicated to collect i-th application data, node u selects at least k stashing nodes from Tisuch that it can forward at least k copies of its i-application data to them. The goal of u is to minimize the total routing cost to send all its p application data to the corresponding stashing nodes of p trajectories. We use the expected number of transmissions on a link as the routing cost of the link and the routing cost for a path is the sum of all the link costs of that path. We wish to minimize the sum of the total routing costs of all the nodes. We call this the Minimum Cost Stashing problem and formulate this as a primal-dual problem. We present a 1/2(2f -k + 1)-approximation algorithm using the primal-dual method for approximation algorithms, where f is the maximum size of a trajectory.