Edge Costs Research Articles

A Novel Lyapunov based Dynamic Resource Allocation for UAVs-assisted Edge Computing

Mobile edge computing (MEC), as a key component in the development of IoT and 5G technologies, can provide extra computation resources in edge servers for mobile devices to complete their computation tasks with low latency and high reliability. Considerable efforts on computation offloading and resource allocation have been developed to reduce the energy consumption and computation latency in edge computing. Nonetheless, the system utility of heterogeneous edge computing system (e.g., UAVs-assisted edge computing), in which multiple unmanned aerial vehicles (UAVs) are involved in an edge computing system to serve as edge servers still needs to be further investigated. To this end, in this paper, we propose a novel Lyapunov based Dynamic Resource Allocation (LDRA) for UAVs-assisted Mobile Edge Computing, which can effectively choose suitable edge servers for mobile devices to offload and complete their computation tasks with low system cost and great system utility of UAVs-assisted edge computing system, as well as acceptable computation latency and great reliability for computation tasks of mobile devices. Particularly, a random queue model for edge servers is conducted in our LDRA scheme to support the dynamic of offloaded computation tasks of mobile devices. Additionally, a system cost model of UAVs-assisted edge computing is developed considering the combination of multiple constraints, such as both the mobility of UAVs and mobile devices, energy consumption, communication cost, etc. With the objective of minimizing the system cost and maximizing the system utility in providing edge resources to complete the offloaded computation tasks of mobile devices, by introducing Lyapunov optimization, a dynamic resource allocation scheme is proposed to effectively determine edge servers to offload tasks of mobile devices with considering both the real-time execution state of offloaded tasks in edge servers and states of the communication link. Through analysis and performance evaluations, our results show that our proposed LDRA scheme can achieve a great balance between system cost and system stability. Additionally, our results also demonstrate that our LDRA scheme also can achieve better system utility in comparison with existing schemes.

An efficient tabu search algorithm for the linear ordering problem

Given a directed graph with n vertices, m edges and costs on the edges, the linear ordering problem (LOP) consists of finding a permutation of the vertices so that the total cost of the reverse edges is minimized, where an edge is called a reverse edge if its head vertex is at a position before the tail in the permutation. Known as an NP-hard problem, the LOP has a number of real-world applications such as the analysis of data called industry transaction table or input-output matrix (I/O table) in the field of economy. In this paper, we propose an algorithm based on tabu search for the LOP. We generalize an algorithm called TREE, which was proposed to search for a best solution in the neighborhood efficiently, so that the new algorithm can be incorporated in the tabu search algorithm and can search for a non-tabu best solution in the neighborhood efficiently. Our algorithm also features an adaptive control mechanism of the tabu tenure by using a cycling-detection mechanism based on a probabilistic analysis. Finally, we compare the experimental results of the proposed algorithm with those of an existing iterated local search algorithm (ILS). The proposed algorithm obtained better results than the ILS for many instances.

Joint Optimization With DNN Partitioning and Resource Allocation in Mobile Edge Computing

With the rapid development of computing power and artificial intelligence, IoT devices equipped with ubiquitous sensors are gradually installed with intelligence. People can enjoy many conveniences with intelligent devices, such as face recognition, video understanding, and motion estimation. Currently, deep neural networks are the mainstream technology in intelligent mobile applications. Inspired by DNN model partition schemes, the paradigm of edge computing could be utilized collaboratively to improve the effectiveness of intelligent task execution in IoT devices. However, due to the dynamics of the wireless network environment and the increasing number of IoT devices, a DNN partition policy without adequate consideration would pose a significant challenge to the efficiency of task inference. Moreover, the shortage and high rental cost of edge computing resources make the optimization of DNN-based task execution more difficult. To cope with those situations, we propose a joint method by a self-adaptive DNN partition with cost-effective resource allocation to facilitate collaborative computation between IoT devices and edge servers. Our proposed online algorithm can be proved to ensure the overall rental cost within an upper bound above the optimal solution while guaranteeing the latency for DNN-based task inference. To evaluate the performance of our strategy, we conduct extensive trace-driven illustrative studies and show that the proposed method can achieve sub-optimal results and outperforms other alternative methods.

Quasi-Popular Matchings, Optimality, and Extended Formulations

Let [Formula: see text] be an instance of the stable marriage problem in which every vertex ranks its neighbors in a strict order of preference. A matching [Formula: see text] in [Formula: see text] is popular if [Formula: see text] does not lose a head-to-head election against any matching. Popular matchings generalize stable matchings. Unfortunately, when there are edge costs, to find or even approximate up to any factor a popular matching of minimum cost is NP-hard. Let [Formula: see text] be the cost of a min-cost popular matching. Our goal is to efficiently compute a matching of cost at most [Formula: see text] by paying the price of mildly relaxing popularity. Our main positive results are two bicriteria algorithms that find in polynomial time a “quasi-popular” matching of cost at most [Formula: see text]. Moreover, one of the algorithms finds a quasi-popular matching of cost at most that of a min-cost popular fractional matching, which could be much smaller than [Formula: see text]. Key to the other algorithm is a polynomial-size extended formulation for an integral polytope sandwiched between the popular and quasi-popular matching polytopes. We complement these results by showing that it is NP-hard to find a quasi-popular matching of minimum cost and that both the popular and quasi-popular matching polytopes have near-exponential extension complexity.

Two-level hub Steiner trees

We study a fundamental class of two-layer network design problems. A hub layer is configured by establishing hubs at selected nodes at considerable cost so that the routes between hubs can be operated cheaply. The remaining edges in the network are operated at regular cost. The resulting problem is to determine the set of nodes to open hubs and the set of edges to establish in order to find a network of minimum total cost.We consider the case where the network is required to form a Steiner tree spanning a given set of terminal vertices. When edge costs are non-metric, we show logarithmic approximation hardness even for the special case of spanning trees. On the other hand, we show a polynomial-time reduction for Steiner trees to its corresponding node-weighted version thus proving a logarithmic approximation factor. When edge costs are metric, we show the problem is only a constant factor harder to approximate than its original version (with no hub installation) using a similar reduction.

Multi-Agent Path Finding with heterogeneous edges and roundtrips

Multi-Agent Path Finding (MAPF) aims to find a set of conflict-free paths for multiple agents on a given graph from parking locations to specified goal locations while optimizing related costs. Currently, existing MAPF studies often consider the simplified problem setup where each agent does not return to its parking location after completing its task on the underlying graph with uniform edge costs. Nevertheless, within some real-word scenarios such as the Unmanned Aircraft System (UAS), agents are situated in the underlying graph with non-uniform edge costs. These agents are required to travel from their respective parking locations to complete tasks, and then return without conflicts. Therefore, this paper explores a new version of MAPF, formally called Multi-Agent Path Finding with Heterogeneous edges and Roundtrips (MAPF-HR). In this version, all agents are engaged in completing tasks by navigating their respective conflict-free paths with roundtrips on the graph with heterogeneous edges. This paper investigates a novel algorithm for this problem, called Improved Conflict-Based Search (CBS) with Helpful Bypass (ICBS-HB), which improves the CBS framework by utilizing the scheme of bypassing conflicts during path finding execution. With extensive experiments on MAPF benchmark maps, it shows that ICBS-HB outperforms the state-of-the-art algorithms for dealing with MAPF-HR.

Approximation Algorithms for the Bottleneck Asymmetric Traveling Salesman Problem

We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem . Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that minimizes its bottleneck (or maximum-length edge) cost. We achieve an O (log n / log log n ) approximation performance guarantee by giving a novel algorithmic technique to shortcut Eulerian circuits while bounding the lengths of the shortcuts needed. This allows us to build on a related result of Asadpour, Goemans, Mądry, Oveis Gharan, and Saberi to obtain this guarantee. Furthermore, we show how our technique yields stronger approximation bounds in some cases, such as the bounded orientable genus case studied by Oveis Gharan and Saberi. We also explore the possibility of further improvement upon our main result through a comparison to the symmetric counterpart of the problem.

Trends in outcomes, cost, and readmissions of transcatheter edge to edge repair in the United States (2014-2018).

Despite the growth in transcatheter edge-to-edge repair (TEER) volume in the United States, data on the temporal changes in procedural outcomes are lacking. We utilized the National Readmission Database to assess the annual changes in patient's characteristics, in-hospital outcomes, cost, and readmissions for patients who underwent TEER between January 1, 2014 and December 31, 2018. Outcomes of interest included mortality, major adverse cardiovascular events (MACE) and any adverse event (AE). We also assessed length of stay and cost. A total of 22,692 hospitalizations were included. The mean age increased from 75.2 ± 12.9 in 2014 to 78.1 ± 9.8 years in 2018. Changes in the prevalence of risk factors were heterogenous. The incidence of in-hospital mortality decreased from 4.0% in 2014 to 2.0% in 2018. Both MACE and any AE decreased significantly. Although the incidence of 30-day readmission remained stable, there was a trend towards a temporal increase in both 90-day and 180-day. The adjusted median length of stay of the index admission decreased by 50% and this trend was associated with a $2100 reduction in risk and inflation adjusted in-hospital cost, however, this reduction was offset by the increased total cost of readmissions within the first 6months resulting in similar net-cost. The volume of TEER has grown substantially between 2014 and 2018 coupled with a temporal improvement in in-hospital outcomes and reduction in cost and length of stay. Re-hospitalization rates after TEER remained steady at 30-day and trended towards worsening overtime at 90- and 180-days.

Minimizing Node Expansions in Bidirectional Search with Consistent Heuristics

A* is optimally effective with regard to node expansions among unidirectional admissible algorithms—those that only assume that the heuristic used is admissible. Among bidirectional algorithms the Fractional MM algorithm is optimally effective (given the correct parameters) among admissible algorithms.This paper generalizes the bidirectional result to more complex settings where more information on the problem domain can be exploited: (1) When the cost of the minimal edge is known. (2) When the algorithm knows that the heuristics are consistent. This characterization uses a novel algorithm called MT. MT is similar to Fractional MM and is also optimally effective, but simpler to analyze.

GBFHS: A Generalized Breadth-First Heuristic Search Algorithm

Recently there has been renewed interest in bidirectional heuristic search. New algorithms, e.g., MM, MMe, and NBS, have been introduced which seem much closer to refuting the accepted wisdom that "any front-to-end bidirectional heuristic search algorithm will likely be dominated by unidirectional heuristic search or bidirectional brute-force search". However, MM and MMe can still be dominated by their bidirectional brute-force versions, i.e., they can show a "hump-in-the-middle". We introduce a novel general breadth-first heuristic search algorithm, GBFHS, that unifies both unidirectional and bidirectional search into a single algorithm. It uses knowledge of the edge cost in unit cost domains to stop on first-collision in unidirectional search and in bidirectional search, unlike MM, MMe, and NBS. With no heuristic it expands fewer nodes bidirectionally than Nicholson's blind bidirectional search algorithm. GBFHS expands substantially fewer nodes than MM0, MM, MMe, and NBS. Additionally, GBFHS does not show a "hump-in-the-middle". GBFHS run bidirectionally is not dominated by bidirectional brute-force search, likewise, GBFHS run unidirectionally is not dominated by A*.

Dynamic Potential Search — A New Bounded Suboptimal Search

Potential Search (PS) is an algorithm that is designed to solve bounded cost search problems. In this paper, we modify PS to work within the framework of bounded suboptimal search and introduce Dynamic Potential Search (DPS). DPS uses the idea of PS but modifies the bound to be the product of the minimal f-value in OPEN and the required suboptimal bound. We study DPS and its attributes. We then experimentally compare DPS to WA* and to EES on a variety of domains and study parameters that affect the behavior of these algorithms.In general we show that in domains with unit edge costs (e.g., many standard benchmarks) DPS significantly outperforms WA* and EES but there are exceptions.

Anytime Tree-Restoring Weighted A* Graph Search

Incremental graph search methods reuse information from previous searches in order to minimize redundant computation and to find solutions to series of similar search queries much faster than it is possible by solving each query from scratch. In this work, we present a simple, but very effective, technique for performing incremental weighted A* graph search in an anytime fashion. On the theoretical side, we show that our anytime incremental algorithm preserves the strong theoretical guarantees provided by the weighted A* algorithm, such as completeness and bounds on solution cost sub-optimality. We also show that our algorithm can handle a variety of changes to the underlying graph, such as both increasing and decreasing edge costs, and changes in the heuristic. On the experimental side, we demonstrate the effectiveness of our algorithm in the context of (x, y, z, yaw) navigation planning for an unmanned aerial vehicle and compare our algorithm to popular incremental and anytime graph search algorithms.

An Improved Meet in the Middle Algorithm for Graphs with Unit Costs

This paper proves several new properties of the Meet in the Middle (MMe) bidirectional heuristic search algorithm when applied to graphs with unit edge costs. Primarily, it is shown that the length of the first path discovered by MMe never exceeds the optimal length by more than one and that if the length of the first path found is odd, then it must be optimal. These properties suggest that the search strategy should emphasize finding a complete path as soon as possible. Computational experiments demonstrate that fully exploiting these new properties can decrease the number of nodes expanded by anywhere from twofold to over tenfold.

Bounded Suboptimal Heuristic Search in Linear Space

It is commonly appreciated that solving search problems optimally can overrun time and memory constraints. Bounded suboptimal search algorithms trade increased solution cost for reduced solving time and memory consumption. However, even suboptimal search can overrun memory on large problems. The conventional approach to this problem is to combine a weighted admissible heuristic with an optimal linear space algorithm, resulting in algorithms such as Weighted IDA* (wIDA*). However, wIDA* does not exploit distance-to-go estimates or inadmissible heuristics, which have recently been shown to be helpful for suboptimal search. In this paper, we present a linear space analogue of Explicit Estimation Search (EES), a recent algorithm specifically designed for bounded suboptimal search. We call our method Iterative Deepening EES (IDEES). In an empirical evaluation, we show that IDEES dramatically outperforms wIDA* on domains with non-uniform edge costs and can scale to problems that are out of reach for the original EES.

An improved algorithm for the Steiner tree problem with bounded edge-length

This work firstly studies the Steiner tree problem with bounded edge-length d in which d is the ratio of the maximum edge cost to the minimum edge cost. This work analyzes the algorithm of Byrka et al. [19] and shows that the approximation ratio of dln⁡4d+ln⁡4−1+ϵ for general graphs and approximation ratio of 73⋅d60⋅d+13+ϵ for quasi-bipartite graphs. The algorithm implies approximation ratio of 1.162+ϵ for the problem on complete graphs with edge distances 1 and 2. This finding represents an improvement upon the previous best approximation ratio of 1.25. This work then presents a combinatorial two-phase heuristic for the general Steiner tree in greedy strategy that achieves an approximation ratio of 1.4295.

Semantic and edge-based visual odometry by joint minimizing semantic and edge distance error

In recent years, the progress made in deep learning for semantic segmentation has advanced development of semantic visual odometry (VO). Along with point-based and direct methods, VO has recently used edge features. However, mismatches are common in scenes in which the distribution of edges is complex owing to the lack of appropriate descriptors for edges at the present. In this paper, we propose a semantic-segmentation-aided edge-based VO (DSEVO). It is intended to improve the localization accuracy by decreasing mismatches in the edge alignment. In the reprojection process, the semantic and edge distance residual are considered to reduce the mismatches of edges between different frames. Then, camera motion estimation is accomplished by jointly minimizing the semantic and edge cost function. Our proposed method was evaluated on the public VKITTI and TUM RGB-D datasets. It was compared with state-of-the-art methods, including the respective feature-point-based, direct, and edge-based methods. We implemented a semantic-edge-based VO system. The experimental results showed that our method achieved the highest accuracy on most of the testing sequences.

Cable tree wiring - benchmarking solvers on a real-world scheduling problem with a variety of precedence constraints

Cable trees are used in industrial products to transmit energy and information between different product parts. To this date, they are mostly assembled by humans and only few automated manufacturing solutions exist using complex robotic machines. For these machines, the wiring plan has to be translated into a wiring sequence of cable plugging operations to be followed by the machine. In this paper, we study and formalize the problem of deriving the optimal wiring sequence for a given layout of a cable tree. We summarize our investigations to model this cable tree wiring problem (CTW). as a traveling salesman problem with atomic, soft atomic, and disjunctive precedence constraints as well as tour-dependent edge costs such that it can be solved by state-of-the-art constraint programming (CP), Optimization Modulo Theories (OMT), and mixed-integer programming (MIP). solvers. It is further shown, how the CTW problem can be viewed as a soft version of the coupled tasks scheduling problem. We discuss various modeling variants for the problem, prove its NP-hardness, and empirically compare CP, OMT, and MIP solvers on a benchmark set of 278 instances. The complete benchmark set with all models and instance data is available on github and was included in the MiniZinc challenge 2020.

Graph transformation and shortest paths algorithms for finite Markov chains.

The graph transformation (GT) algorithm robustly computes the mean first-passage time to an absorbing state in a finite Markov chain. Here we present a concise overview of the iterative and block formulations of the GT procedure and generalize the GT formalism to the case of any path property that is a sum of contributions from individual transitions. In particular, we examine the path action, which directly relates to the path probability, and analyze the first-passage path ensemble for a model Markov chain that is metastable and therefore numerically challenging. We compare the mean first-passage path action, obtained using GT, with the full path action probability distribution simulated efficiently using kinetic path sampling, and with values for the highest-probability paths determined by the recursive enumeration algorithm (REA). In Markov chains representing realistic dynamical processes, the probability distributions of first-passage path properties are typically fat-tailed and therefore difficult to converge by sampling, which motivates the use of exact and numerically stable approaches to compute the expectation. We find that the kinetic relevance of the set of highest-probability paths depends strongly on the metastability of the Markov chain, and so the properties of the dominant first-passage paths may be unrepresentative of the global dynamics. Use of a global measure for edge costs in the REA, based on net productive fluxes, allows the total reactive flux to be decomposed into a finite set of contributions from simple flux paths. By considering transition flux paths, a detailed quantitative analysis of the relative importance of competing dynamical processes is possible even in the metastable regime.

G-Value Plateaus: A Challenge for Planning

While the string of successes found in using heuristic, best-first search methods have provided positive reinforcement for continuing work along these lines, fundamental problems arise when handling objectives whose value does not change with search operations. An extreme case of this occurs when handling the objective of generating a temporal plan with short makespan. Typically used heuristic search methods assume strictly positive edge costs for their guarantees on completeness and optimality, while the usual ``fattening'' and ``advance time'' steps of heuristic search for temporal planning have the potential of resulting in ``g-value plateaus''. In this paper we point out some underlying difficulties with using modern heuristic search methods when operating over g-value plateaus and discuss how the presence of these problems contributes to the poor performance of heuristic search planners. To further illustrate this, we show empirical results on recent benchmarks using a planner made with makespan optimization in mind.

Across-camera object tracking using a conditional random field model

To ensure safety, most public spaces now deploy monitoring systems. However, in most scenarios, the tracking operations of these monitoring systems are performed manually. These operations should be automated. This paper proposes using a conditional random field (CRF) to formulate the automatic execution problem as a cost minimization problem. The appearance of pedestrians and the time taken by them to cross the view of a camera are used to solve the automatic execution problem. Crowd psychology is used to define constraints and construct a CRF graph. A Siamese convolutional neural network is employed to recognize pedestrian appearance. The time spent by pedestrians crossing the view of a camera is modeled using a normal distribution. The results of two models are considered as the costs of nodes and edges. The proposed algorithm is applied under constraints to determine matches at the minimum cost. The accuracy of the proposed method is compared with that of other methods by using common datasets and benchmarks. Superior results are obtained when both appearance and spatiotemporal information are employed for solving the automatic execution problem than when using appearance alone.