Minimum Weight Path Research Articles

Investigating the min‐cost minimum fleet problem through taxi data analysis

AbstractThe optimization of urban traffic efficiency and reduction of pollution through minimizing the number of taxis has become a topic of increasing interest. However, the problem of determining the minimum fleet that considers both time and distance efficiency has received limited attention. Furthermore, little research has been done on how this problem is influenced by factors such as city size and travel demand (i.e., the number of trips). This study extends the minimum fleet problem to the min‐cost minimum fleet problem, and proposes a method to address the problem by constructing a “dispatch network” and finding the minimum weight and minimum path cover of it. A comparative analysis of the method is conducted with the taxi trajectory data of three cities, New York, Chengdu, and Chicago, and the results show a reduction in the off‐load travel time of vehicles compared to the previous method, while maintaining the same fleet size. With the introduction of an emissions model and its combination with our methodology, emissions can also be minimized. Moreover, the relationship between min‐cost minimum fleet and city size and travel demand (number of trips) is studied. Experimental results indicate that fleet size and idle time (distance) vary linearly with the number of trips. Meanwhile, city size also has an essential impact on the algorithm's performance. Furthermore, these results indicate that the min‐cost minimum fleet will help small cities to achieve higher efficiency (smaller fleet and less connection time) than large cities. The acceleration of urbanization is driving changes in the transportation system. Our findings are expected to have significant implications for transport planning, resource conservation, and reducing pollution.

Accurate summary-based cardinality estimation through the lens of cardinality estimation graphs

This paper is an experimental and analytical study of two classes of summary-based cardinality estimators that use statistics about input relations and small-size joins in the context of graph database management systems: (i) optimistic estimators that make uniformity and conditional independence assumptions; and (ii) the recent pessimistic estimators that use information theoretic linear programs (LPs). We begin by analyzing how optimistic estimators use pre-computed statistics to generate cardinality estimates. We show these estimators can be modeled as picking bottom-to-top paths in a cardinality estimation graph (CEG), which contains sub-queries as nodes and edges whose weights are average degree statistics. We show that existing optimistic estimators have either undefined or fixed choices for picking CEG paths as their estimates and ignore alternative choices. Instead, we outline a space of optimistic estimators to make an estimate on CEGs, which subsumes existing estimators. We show, using an extensive empirical analysis, that effective paths depend on the structure of the queries. While on acyclic queries and queries with small-size cycles, using the maximum-weight path is effective to address the well known underestimation problem, on queries with larger cycles these estimates tend to overestimate, which can be addressed by using minimum weight paths. We next show that optimistic estimators and seemingly disparate LP-based pessimistic estimators are in fact connected. Specifically, we show that CEGs can also model some recent pessimistic estimators. This connection allows us to adopt an optimization from pessimistic estimators to optimistic ones, and provide insights into the pessimistic estimators, such as showing that they have combinatorial solutions.

Задача локальної оптимізації графів та її застосування

Introduction. We study the problem of constructing a locally optimal directed graph when each edge is assigned a fixed numerical weight. Due to the broad interpretation of the numerical weights of edges, the problem of finding the least-cost paths has many applications and is one of the most common and studied problems in the applied theory of algorithms. In various modifications, it can be found in algorithms for constructing optimal routes for flying and other moving objects, in pattern recognition, optimization of communication networks and integrated circuits. The property of local optimality is defined through a dynamic process that at every round assigns to each vertex the minimal value depending on its current value and sums of values stored in neighborhood vertices with weights of incoming edges. The graph is locally optimal when any vertex cannot allow further minimizations. Purpose. The purpose of the article is to investigate the problem of constructing a locally-optimal graph, establish properties of such graphs, and derive new applications. Methods. We consider the problem of finding the shortest paths in a broader context as a general computational problem of local graph optimization. This model of computations on a graph is studied. Each local vertex, regardless of the other vertices, performs the same iterative procedure of minimizing some non-negative numerical value assigned to that vertex. The operation of such minimization depends on the current value obtained in this vertex when applying the previous minimization and sums of the current numerical data located in the vertices from which the input edges lead to the selected local vertex and weights of the seedges. After several stages of such an operation, the graph always comes into a stable state: further minimization of vertices does not change the values assigned to the vertices. In this state, we call the graph locally optimal. Results. The conditions under which the graph reaches the state of local optimization are investigated. With different choices of interpretation of the function that determines the influence of neighboring vertices on the vertex minimization value, we obtain a variety of applications. For example, the gradient descent method from the local optimization state makes it easy to obtain the minimum weight (cost) paths from the given starting vertex to all vertices. If the graph is interpreted as a semantic network in the space of natural language words, it is shown how the problem of finding the minimum path among words or phrases is interpreted as solving a known problem in computational linguistics: find the word most associated with a given input set words or sentences (images). Finally, by calculating the weights of the paths in randomized (uniformly distributed) graphs, a fast-authentication protocol is proposed for the two coalition entities acting in a malicious environment. Conclusions. The local optimality is a stable constant state of the current graph marking reachable by using the dynamic minimization process. Local optimality provides a common method for solving many problems related to search engine optimization. It is shown how from solving the general problem of constructing a locally-optimal graph it follows the problem of finding the paths of least weights (cost). New applications include solving the problem of associative search in computational linguistics (creative thinking) and fast mutual authentication in coalition groups.

Smart Routing Protocol Algorithm Using Fuzzy Artificial Neural Network OSPF

The OSPF cost is proportionally indicated the transmitting packet overhead through a certain interface and inversely proportional to the interface bandwidth. Thus, this cost may minimized by direct packet transmitting to the other side via various probable paths simultaneously. Logically, the minimum weight path is the optimum path. This paper propose a novel Fuzzy Artificial Neural Network to create Smart Routing Protocol Algorithm. Consequently, the Fuzzy Artificial Neural Network Overlap has been reduced from (0.883 ms) to (0.602 ms) at fuzzy membership 1.5 to 4.5 respectively. This indicated the transmission time is two-fold faster than the standard overlapping time (1.3 ms).

Optimal run problem for weighted register automata

Register automata (RA) are a computational model that can handle data values by adding registers to finite automata. Recently, weighted register automata (WRA) were proposed by extending RA so that weights can be specified for transitions. In this paper, we first investigate decidability and complexity of decision problems on the weights of runs in WRA. We then propose an algorithm for the optimal run problem related to the above decision problems. For this purpose, we use a register type as an abstraction of the contents of registers, which is determined by binary relations (such as =, <, etc.) handled by WRA. Also, we introduce a subclass where both the applicability of transition rules and the weights of transitions are determined only by a register type. We present a method of transforming a given WRA satisfying the assumption to a weighted directed graph such that the optimal run of WRA and the minimum weight path of the graph correspond to each other. Lastly, we discuss the optimal run problem for weighted timed automata as an example.

A four-stage adaptive scheduling scheme for service function chain in NFV

Network Function Virtualization (NFV) enables the flexible software implementation of Network Functions (NFs) which is called Virtualized Network Function (VNF) and placed along the routing path of the network flow. A sequence of VNFs constitutes a Service Function Chain (SFC) to satisfy the processing requirements of flows. Since the SFC scheduling depends on the current network state and the dynamics of flows, it brings a great challenge to make an optimal SFC scheduling decision efficiently. In this paper, we present a Four-stage Adaptive Scheduling Scheme (FSASM) to make a trade-off between different scheduling goals and effects on network performance and management overhead. We design the specific mechanism for each stage when the network is in different workloads. Then, we prove the NP hardness of the optimization models in FSASM and propose a Minimum wEight Path Selection Algorithm (MEPS) with polynomial time complexity to realize a practical SFC scheduling. Moreover, we perform comprehensive experiments under different real-world topologies and network states. The results demonstrate that FSASM can achieve high network throughput and resource utilization as well as decrease the scaling frequency in highly dynamic network scenarios.

Design of General Entropy-Constrained Successively Refinable Unrestricted Polar Quantizer

This paper presents an algorithm for the optimal design of general entropy-constrained successively refinable unrestricted polar quantizer, i.e., with arbitrary number $L$ of refinement levels, for bivariate circularly symmetric sources. The optimization problem is formulated as the minimization of a weighted sum of distortions and entropies for the scenario where the magnitude quantizers’ thresholds are confined to a predefined finite set. The proposed solution algorithm is globally optimal. It involves $L$ stages, where each stage corresponds to an unrestricted polar quantizer (UPQ) level, and includes solving the minimum-weight path problem for multiple node pairs in a series of weighted directed acyclic graphs. Additionally, we derive an upper bound $P^{(l)}_{\max }, l\in [1:L]$ , on the possible number of phase levels in any phase quantizer of the $l$ -th level UPQ, which grows linearly with $l$ . The time complexity of the proposed approach is $O(L^{2}K^{3} P^{(1)}_{\max })$ , where $K$ is the cardinality of the predefined set of possible magnitude thresholds. Finally, the experimental results for $L=3$ demonstrate the effectiveness in practice of the proposed scheme.

Marine Observation Beacon Clustering and Recycling Technology Based on Wireless Sensor Networks.

Monitoring of marine polluted areas is an emergency task, where efficiency and low-power consumption are challenging for the recovery of marine monitoring equipment. Wireless sensor networks (WSNs) offer the potential for low-energy recovery of marine observation beacons. Reducing and balancing network energy consumption are major problems for this solution. This paper presents an energy-saving clustering algorithm for wireless sensor networks based on k-means algorithm and fuzzy logic system (KFNS). The algorithm is divided into three phases according to the different demands of each recovery phase. In the monitoring phase, a distributed method is used to select boundary nodes to reduce network energy consumption. The cluster routing phase solves the extreme imbalance of energy of nodes for clustering. In the recovery phase, the inter-node weights are obtained based on the fuzzy membership function. The Dijkstra algorithm is used to obtain the minimum weight path from the node to the base station, and the optimal recovery order of the nodes is obtained by using depth-first search (DFS). We compare the proposed algorithm with existing representative methods. Experimental results show that the algorithm has a longer life cycle and a more efficient recovery strategy.

Design of Successively Refinable Unrestricted Polar Quantizer

This paper addresses the design of two-stage successively refinable unrestricted polar quantizers for bivariate circularly symmetric sources in the entropy-constrained and fixed-rate cases. The proposed solutions are globally optimal when the thresholds of the magnitude quantizers are confined to finite discretizations of the interval $\left[0,\infty\right)$ . The algorithm developed for the entropy-constrained case involves a series of stages, including solving the minimum-weight path problem for multiple node pairs in certain weighted directed acyclic graphs. The asymptotical time complexity is ${O}({K}_{1}{K}_{2}^{2}{P}_{max})$ , where ${K}_{1}$ and ${K}_{2}$ are the sizes of the sets of possible magnitude thresholds of the coarse and refined unrestricted polar quantizers (UPQs), respectively, while ${P}_{max}$ is an upper bound on the number of phase levels in any phase quantizer of the coarse UPQ. The solution algorithm for the fixed-rate case is based on solving a succession of dynamic programming problems for multiple coarse quantizer bins. The time complexity in the fixed-rate case amounts to ${O}({K}_{1}{K}_{2}{N}^{2}{N}_{1})$ , where ${N}_{1}$ is the number of cells of the coarse UPQ and $N$ is the ratio between the number of bins of the fine and coarse UPQs. The extensive experimental results on a bivariate circularly symmetric Gaussian source show the effectiveness of the proposed schemes.

Fuzzy-Logic Dijkstra-Based Energy-Efficient Algorithm for Data Transmission in WSNs.

In wireless sensor networks, clustering routing algorithms have been widely used owing to their high energy-efficiency and scalability. In clustering schemes, the nodes are organized in the form of clusters, and each cluster is governed by a cluster head. Once the cluster heads are selected, they form a backbone network to periodically collect, aggregate, and forward data to the base station using minimum energy (cost) routing. This approach significantly improves the network lifetime. Therefore, a new cluster head selection method that uses a weighted sum method to calculate the weight of each node in the cluster and compare it with the standard weight of that particular cluster is proposed in this paper. The node with a weight closest to the standard cluster weight becomes the cluster head. This technique balances the load distribution and selects the nodes with highest residual energy in the network. Additionally, a data routing scheme is proposed to determine an energy-efficient path from the source to the destination node. This algorithm assigns a weight function to each link on the basis of a fuzzy membership function and intra-cluster communication cost within a cluster. As a result, a minimum weight path is selected using Dijkstra’s algorithm that improves the energy efficiency of the overall system. The experimental results show that the proposed algorithm shows better performance than some existing representative methods in the aspects of energy consumption, network lifetime, and system throughput.

Optimal Design of a Two-Stage Wyner-Ziv Scalar Quantizer With Forwardly/Reversely Degraded Side Information

This paper addresses the optimal design of a two-stage Wyner-Ziv scalar quantizer with forwardly or reversely degraded side information (SI) for finite-alphabet sources and SI. We assume that the binning is performed optimally and address the design of the quantizer partitions. The optimization problem is formulated as the minimization of a weighted sum of distortions and rates. The proposed solution is globally optimal when the cells in each partition are contiguous. The solution algorithm is based on solving the single-source or the all-pairs minimum-weight path (MWP) problem in certain weighted directed acyclic graphs. When the conventional dynamic programming technique is used to solve the underlying MWP problems, the time complexity achieved is O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ), where N is the size of the source alphabet. A so-called partial Monge property is additionally introduced, and a faster solution algorithm exploiting this property is proposed. Experimental results assess the practical performance of the proposed scheme.

Design of Optimal Scalar Quantizer for Sequential Coding of Correlated Sources

This paper addresses the design of a sequential scalar quantizer (SSQ) for finite-alphabet correlated sources in the fixed-rate (FR) and entropy-constrained (EC) cases. The optimization problem is formulated as the minimization of a weighted sum of distortions and rates. The proposed solution is globally optimal for the class of SSQs with convex cells and is based on solving the minimum-weight path (MWP) problem in the EC case, respectively, a length-constrained MWP problem in the FR case, in a series of weighted directed acyclic graphs. The asymptotic time complexity is $O(K_{1}^{2}K_{2}^{2})$ , where $K_{1}$ and $K_{2}$ are the respective sizes of the alphabets of the two sources. Additionally, it is proved that, by applying the proposed algorithms to discretizations of correlated sources with continuous joint probability density function, the performance approaches that of the optimal EC-SSQ, respectively, FR-SSQ, with convex cells for the original sources as the accuracy of the discretization increases. Extensive experiments performed with correlated Gaussian sources validate the effectiveness in practice of the proposed approach in approximating the optimal SSQ for the case of continuous-alphabet sources.

Load-Balancing Routing Algorithm Based on Segment Routing for Traffic Return in LEO Satellite Networks

To tackle the network congestion problem caused by ground gateway stations arranged within a limited area in low earth orbit (LEO) satellite networks, a routing algorithm based on segment routing for traffic return is proposed. Light and heavy load zones are dynamically divided according to the relative position relationship between gateways and the reverse slot. The pre-balancing shortest path algorithm is used in the light load zone, and the minimum weight path defined by congestion index is the routing rule in the heavy load zone. Then, the consistent forwarding is performed referring to segment routing in all zones. Simulation conditions are different sizes of heavy load zone, different traffic density distributions, and different traffic demands. Simulation results confirm that the load-balancing performance is improved significantly with the extension of the heavy load zone size in terms of the average rejection ratio, the average relative throughput, the maximum link utilization, and the average delay. The proposed algorithm is an alternative solution and guidance for routing strategy in LEO satellite networks.

Negligence Minimum Spanning Tree Algorithm

In the life, we always aim to do anything with the less cost considering time and distance. In graph theory, finding a minimum weight (cost or path) is a well-known problem. A minimum spanning tree is one of the methods brought for this purpose. In this work, we consider a negligence algorithm to find a minimum spanning tree in another way. We report a comparison between our algorithm and Kruskal's MST algorithm. We implemented some examples of the graphs to get the results in less time and more effectively.

INFERRING ROUTING PREFERENCES OF BICYCLISTS FROM SPARSE SETS OF TRAJECTORIES

Abstract. Understanding the criteria that bicyclists apply when they choose their routes is crucial for planning new bicycle paths or recommending routes to bicyclists. This is becoming more and more important as city councils are becoming increasingly aware of limitations of the transport infrastructure and problems related to automobile traffic. Since different groups of cyclists have different preferences, however, searching for a single set of criteria is prone to failure. Therefore, in this paper, we present a new approach to classify trajectories recorded and shared by bicyclists into different groups and, for each group, to identify favored and unfavored road types. Based on these results we show how to assign weights to the edges of a graph representing the road network such that minimumweight paths in the graph, which can be computed with standard shortest-path algorithms, correspond to adequate routes. Our method combines known algorithms for machine learning and the analysis of trajectories in an innovative way and, thereby, constitutes a new comprehensive solution for the problem of deriving routing preferences from initially unclassified trajectories. An important property of our method is that it yields reasonable results even if the given set of trajectories is sparse in the sense that it does not cover all segments of the cycle network.

The shortest kinship description problem

We consider a problem in descriptive kinship systems, namely finding the shortest sequence of terms that describes the kinship between a person and his/her relatives. The problem reduces to finding the minimum weight path in a labeled graph where the label of the path comes from a regular language. The running time of the algorithm is O(n3+s), where n and s are the input size and the output size of the algorithm, respectively.

Design of Optimal Entropy-Constrained Unrestricted Polar Quantizer for Bivariate Circularly Symmetric Sources

This paper proposes an algorithm for the design of entropy-constrained unrestricted polar quantizer (ECUPQ) for bivariate circularly symmetric sources. The algorithm is globally optimal for the class of ECUPQs with magnitude quantizer thresholds confined to a finite set. The optimization problem is formulated as the minimization of a weighted sum of distortion and entropy, and the proposed solution is based on modeling the problem as a minimum-weight path problem in a certain weighted directed acyclic graph. Each graph edge corresponds to a possible magnitude quantizer bin and computing its weight involves solving another optimization problem. We develop a fast strategy for evaluating all edge weights, leading to a $O(K^{2}+\textit {KP}_{\mathrm{ max}})$ time solution algorithm, where $K$ is the size of the set of possible magnitude thresholds and $P_{\mathrm{ max}}$ is the maximum number of phase levels. The practical performance of the proposed algorithm is assessed for a bivariate circularly symmetric Gaussian source, at rates ranging from 0.5 to 6 bits/sample. Our results demonstrate that the proposed approach achieves performance very close to the asymptotically optimal ECUPQ at all rates, while at low rates it significantly outperforms all previous UPQ schemes. Notably, peak improvement of 0.755 dB can be achieved for rates below 2.5.

Applying Fuzzy Artificial Neural Network OSPF to develop Smart Routing Protocol Algorithm

The OSPF cost is proportionally indicated the transmitting packet overhead through a certain interface and inversely proportional to the interface bandwidth. Thus, this cost may minimized by direct packet transmitting to the other side via various probable paths simultaneously. Logically, the minimum weight path is the optimum path. This paper propose a novel Fuzzy Artificial Neural Network to create Smart Routing Protocol Algorithm. Consequently, the Fuzzy Artificial Neural Network Overlap has been reduced from (0.883 ms) to (0.602 ms) at fuzzy membership 1.5 to 4.5 respectively. This indicated the transmission time is two-fold faster than the standard overlapping time (1.3 ms).

Universality for first passage percolation on sparse random graphs

We consider rst passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satises a uniform X 2 logX-condition, we analyze the asymptotic distribution for the minimal weight path between a pair of typical vertices, as well the number of edges on this path or hopcount. The hopcount satises a central limit theorem where the norming constants are expressible in terms of the parameters of an associated continuous-time branching process. Centered by a multiple of logn, where the constant is the inverse of the Malthusian rate of growth of the associated branching process, the minimal weight converges in distribution. The limiting random variable equals the sum of the logarithms of the martingale limits of the branching processes that measure the relative growth of neighborhoods about the two vertices, and a Gumbel random variable, and thus shows a remarkably universal behavior. The proofs rely on a rened coupling between the shortest path problems on these graphs and continuous-time branching processes, and on a Poisson point process limit for the potential closing edges of shortest-weight paths between the source and destination. The results extend to a host of related random graph models, ranging from random rregular graphs, inhomogeneous random graphs and uniform random graphs with a prescribed degree sequence.

First Passage Percolation on Inhomogeneous Random Graphs

In this paper we investigate first passage percolation on an inhomogeneous random graph model introduced by Bollobáset al.(2007). Each vertex in the graph has a type from a type space, and edge probabilities are independent, but depend on the types of the end vertices. Each edge is given an independent exponential weight. We determine the distribution of the weight of the shortest path between uniformly chosen vertices in the giant component and show that the hopcount, i.e. the number of edges on this minimal-weight path, properly normalized, follows a central limit theorem. We handle the cases where the average number of neighbors λ̃nof a vertex tends to a finite λ̃ in full generality and consider λ̃ = ∞ under mild assumptions. This paper is a generalization of the paper of Bhamidiet al.(2011), where first passage percolation is explored on the Erdős-Rényi graphs.