Exponential Complexity Research Articles

Non-Intrusive Privacy-Preserving Approach for Presence Monitoring Based on WiFi Probe Requests

Monitoring the presence and movements of individuals or crowds in a given area can provide valuable insight into actual behavior patterns and hidden trends. Therefore, it is crucial in areas such as public safety, transportation, urban planning, disaster and crisis management, and mass events organization, both for the adoption of appropriate policies and measures and for the development of advanced services and applications. In this paper, we propose a non-intrusive privacy-preserving detection of people's presence and movement patterns by tracking their carried WiFi-enabled personal devices, using the network management messages transmitted by these devices for their association with the available networks. However, due to privacy regulations, various randomization schemes have been implemented in network management messages to prevent easy discrimination between devices based on their addresses, sequence numbers of messages, data fields, and the amount of data contained in the messages. To this end, we proposed a novel de-randomization method that detects individual devices by grouping similar network management messages and corresponding radio channel characteristics using a novel clustering and matching procedure. The proposed method was first calibrated using a labeled publicly available dataset, which was validated by measurements in a controlled rural and a semi-controlled indoor environment, and finally tested in terms of scalability and accuracy in an uncontrolled crowded urban environment. The results show that the proposed de-randomization method is able to correctly detect more than 96% of the devices from the rural and indoor datasets when validated separately for each device. When the devices are grouped, the accuracy of the method decreases but is still above 70% for rural environments and 80% for indoor environments. The final verification of the non-intrusive, low-cost solution for analyzing the presence and movement patterns of people, which also provides information on clustered data that can be used to analyze the movements of individuals, in an urban environment confirmed the accuracy, scalability and robustness of the method. However, it also revealed some drawbacks in terms of exponential computational complexity and determination and fine-tuning of method parameters, which require further optimization and automation.

A novel image encryption scheme based on Logistic cosine cascade maps

A two-dimensional Logistic cosine cascade map (2D-LCCM) and a three-dimensional Logistic cosine cascade map (3D-LCCM) are proposed based on a logistic map and infinite collapse cascade model. We analyze the chaotic properties of 2D-LCCM and 3D-LCCM, such as Lyapunov exponential spectrum, attractors, and complexity, which show that the 2D-LCCM and 3D-LCCM are hyperchaotic and have large chaotic regions. We also proposed a DNA encryption algorithm based on double chaotic maps. 2D-LCCM was used for scrambling and 3D-LCCM for diffusion. First, the sequence no-duplicate zigzag transform (SNZT) is used to scramble the plaintext. Z-transform is applied to the permutation sequence to make the sequence more random. Then a repetition-free permutation associated with the plaintext is applied to each block, and the pixel position is effectively scrambled. Finally, DNA diffusion is performed using DNA coding to diffuse pixel values. Simulation results show that the algorithm has a good encryption effect, high efficiency and anti-interference performance. Therefore, the proposed new hyperchaotic map and DNA encryption algorithm can be effectively applied to the process of image encryption.

Mission planning on preference-based expression trees using heuristics-assisted evolutionary computation

The mission planning problem has so far been solved by using temporal logic and classic planning approaches that have an exponential computational complexity and do not always account for the transition costs. Variants of the Vehicle Routing Problem can use meta-heuristics to give a near-optimal solution; however, have a limited representation capability. In this paper the problem of giving complex instructions (mission) to a robot in the form of an expression tree with AND, OR and THEN operators is studied. This allows users to instruct the robots for everyday tasks like getting a variety of items (modeled by AND) with a few choices (modeled by OR), the picks having temporal constraints (modeled by THEN). Preferences can be added to make the robot solve a sub-mission earlier than another sub-mission. The paper first proposes an algorithm to make a greedy solution by a single parse of the expression tree. Thereafter, the solution is optimized by using a Genetic Algorithm that optimizes the branch to be taken by the OR operator and the ordering of operations. Experimental results are demonstrated on the Pioneer LX robot programmed using the Robot Operating System. The experimental results further show that the proposed approach significantly beats a Genetic Algorithm solution and a Dynamic Programming greedy solution for problem sizes that cannot be solved by using the model verification and exhaustive search techniques.

Recommender system for ablation lines to treat complex atrial tachycardia

Background and Objective: Planning the optimal ablation strategy for the treatment of complex atrial tachycardia (CAT) is a time consuming task and is error-prone. Recently, directed network mapping, a technology based on graph theory, proved to efficiently identify CAT based solely on data of clinical interventions. Briefly, a directed network was used to model the atrial electrical propagation and reentrant activities were identified by looking for closed-loop paths in the network. In this study, we propose a recommender system, built as an optimization problem, able to suggest the optimal ablation strategy for the treatment of CAT.Methods: The optimization problem modeled the optimal ablation strategy as that one interrupting all reentrant mechanisms while minimizing the ablated atrial surface. The problem was designed on top of directed network mapping. Considering the exponential complexity of finding the optimal solution of the problem, we introduced a heuristic algorithm with polynomial complexity. The proposed algorithm was applied to the data of i) 6 simulated scenarios including both left and right atrial flutter; and ii) 10 subjects that underwent a clinical routine.Results: The recommender system suggested the optimal strategy in 4 out of 6 simulated scenarios. On clinical data, the recommended ablation lines were found satisfactory on 67% of the cases according to the clinician’s opinion, while they were correctly located in 89%. The algorithm made use of only data collected during mapping and was able to process them nearly real-time.Conclusions: The first recommender system for the identification of the optimal ablation lines for CAT, based solely on the data collected during the intervention, is presented. The study may open up interesting scenarios for the application of graph theory for the treatment of CAT.

Experimental Demonstration of Quantum Overlapping Tomography

Quantum tomography is one of the major challenges of large-scale quantum information research due to the exponential time complexity. In this Letter, we develop and apply a Bayesian state estimation method to experimentally demonstrate quantum overlapping tomography [Phys. Rev. Lett. 124, 100401 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.100401], a scheme intent on characterizing critical information of a many-body quantum system in logarithmic time complexity. By comparing the measurement results of full-state tomography and overlapping tomography, we show that overlapping tomography gives accurate information of the system with much fewer state measurements than full-state tomography.

Towards Efficient Large-Scale Network Slicing: An LP Dynamic Rounding-and-Refinement Approach

In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network resources to meet diverse service requirements. The problem has been formulated as a mixed integer linear programming (MILP) formulation in the literature. We first propose a novel linear programming (LP) relaxation of the MILP formulation. We show that compared with a natural LP relaxation of the MILP formulation, the novel LP relaxation is much more compact in terms of smaller numbers of variables and constraints, and much stronger in terms of providing a better LP bound, which makes it particularly suitable to be embedded in an LP relaxation based algorithm. Then we design an efficient two-stage LP dynamic rounding-and-refinement algorithm based on this novel LP relaxation. In the first stage, the proposed algorithm uses an LP dynamic rounding procedure to place the virtual network functions of all services into cloud nodes while taking traffic routing of all services into consideration; in the second stage, the proposed algorithm uses an iterative LP refinement procedure to obtain a solution for traffic routing of all services with their end-to-end delay constraints being satisfied. Compared with the existing algorithms which either have an exponential complexity or return a low-quality solution, our proposed algorithm achieves a better trade-off between the solution quality and the computational complexity. In particular, the worst-case complexity of our proposed algorithm is polynomial, which makes it suitable for solving large-scale problems. Numerical results demonstrate the effectiveness and efficiency of our proposed algorithm.

Reachability of Linear Time-Invariant Systems via Ellipsoidal Approximations

Reachability analysis is a powerful tool when it comes to capturing the behaviour, thus verifying the safety, of autonomous systems. However, general-purpose methods, such as Hamilton-Jacobi approaches, exhibit exponential computational complexity with respect to the state dimension. In this paper, we show that supersolutions and subsolutions of a Hamilton-Jacobi-Bellman equation can be used to generate under- and over-approximating reachable sets for nonlinear systems, and based on this, we develop a scheme for approximating reachable sets of linear time-invariant systems via ellipsoids with polynomial computational complexity.

Mining Top-k Frequent Patterns in Large Geosocial Networks: A Mnie-Based Extension Approach

Frequent pattern mining (FPM) has played an important role in many graph domains, such as bioinformatics and social networks. In this paper, we focus on geo-social graphs, a kind of social network augmented by geographical information. However, in addition to the exponential time complexity of the problem, we face the challenge of efficient subgraph retrieval since we are interested in patterns in a specific region in such a network. For this reason, we formulate the top-k FPM problem in large geo-social networks. Specifically, we devise a novel framework for subgraph retrieval and FPM mining with a series of optimizations. First, we propose a neighboring-aware R-tree (NaR-Tree) index structure to alleviate the challenge of retrieving subgraphs from a large graph. NaR-Tree is a variant of R-tree in which each nonleaf tree node further maintains some edge statistics information for the rectangle related to it. Second, we define the concept of minimum image-based support of edges (MNIE). With the help of the NaR-Tree and MNIE-based pattern extension approach, a mining algorithm that addresses the problem of exponential candidate patterns is proposed. We also present a lazy retrieval strategy to reduce the frequency of subgraph retrieval. Finally, we adopt an edge sampling approach to further accelerate the mining process. Extensive experiments on real-world and synthesized datasets are conducted to demonstrate the effectiveness and efficiency of our solution.

Early detection of neurological abnormalities using a combined phase space reconstruction and deep learning approach

The scientific literature on depression detection using electroencephalogram (EEG) signals is extensive and offers numerous innovative approaches. However, these existing state-of-the-art (SOTA) have limitations that hinder their overall efficacy. They rely significantly on datasets with limited scope and accessibility, which introduces potential biases and diminishes generalizability. In addition, they concentrate on analyzing a single dataset, potentially overlooking the inherent variability and complexity of EEG patterns associated with depression. Moreover, certain SOTA methods employ deep learning architectures with exponential time complexity, resulting in computationally intensive and time-consuming training procedures. Therefore, their practicability and applicability in real-world scenarios are compromised. To address these limitations, a novel integrated methodology that combines the advantages of phase space reconstruction and deep neural networks is proposed. It employs publicly available EEG datasets, mitigating the inherent biases of exclusive data sources. Moreover, the method incorporates reconstructed phase space analysis, a feature engineering technique that captures more accurately the complex EEG patterns associated with depression. Simultaneously, the incorporation of a deep neural network component guarantees optimal efficiency and accurate, seamless classification. Using publicly available datasets, cross-dataset validation, and a novel combination of reconstructed phase space analysis and deep neural networks, the proposed method circumvents the shortcomings of current state-of-the-art (SOTA) approaches. This innovation represents a significant advance in enhancing the accuracy of depression detection and provides the base for EEG-based depression assessment tools applicable to real-world settings. The findings of the study provide a more robust and efficient model, which increases classification precision and decreases computing burden. The study findings layout the foundation for scalable, accessible mental health solutions, identification of the pathological deficits in affected brain tissues, and demonstrate the potential of technology-driven approaches to support and guide depressed individuals and enhance mental health outcomes.

Projecting basis functions with tensor networks for Gaussian process regression

This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on the total number of basis functions M. We develop an approach that allows us to use an exponential amount of basis functions without the corresponding exponential computational complexity. The key idea to enable this is using low-rank TNs. We first find a suitable low-dimensional subspace from the data, described by a low-rank TN. In this low-dimensional subspace, we then infer the weights of our model by solving a Bayesian inference problem. Finally, we project the resulting weights back to the original space to make GP predictions. The benefit of our approach comes from the projection to a smaller subspace: It modifies the shape of the basis functions in a way that it sees fit based on the given data, and it allows for efficient computations in the smaller subspace. In an experiment with an 18-dimensional benchmark data set, we show the applicability of our method to an inverse dynamics problem.

List Encoding of Vector Perturbation Precoding

In this letter, we propose a new nonlinear precoding algorithm, List encoding of Vector Perturbation precoding (LVP) for Multiple Input Multiple Output (MIMO) system. Different from the traditional VP based on sphere search strategy to minimize the Frobeniuas norm of the precoded signal with a exponential search complexity, LVP adopts multiple encoders design, a list of encoder perform only one dimensional integer optimization through several iterations in parallel. During each iteration each encoder searches through several perturbation results and retain one of them to the next iteration. When the iterations ends, the historical optimal perturbation result with the least Frobenius norm is output as the precoding result. The search complexity of LVP is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(M)$</tex-math></inline-formula> which increases linearly with the antenna number <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> . This complexity is much smaller than sphere search based strategy. Compared with other low dimensional search algorithm represented by D2VP, the search complexity drops from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(M^{2})$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(M)$</tex-math></inline-formula> , with a significant BER gain thanks to the multiple encoder design. To the best of our knowledge, with similar BER performance the LVP algorithm has the lowest complexity.

Efficient simplicial replacement of semialgebraic sets

Abstract Designing an algorithm with a singly exponential complexity for computing semialgebraic triangulations of a given semialgebraic set has been a holy grail in algorithmic semialgebraic geometry. More precisely, given a description of a semialgebraic set $S \subset \mathbb {R}^k$ by a first-order quantifier-free formula in the language of the reals, the goal is to output a simplicial complex $\Delta $ , whose geometric realization, $|\Delta |$ , is semialgebraically homeomorphic to S. In this paper, we consider a weaker version of this question. We prove that for any $\ell \geq 0$ , there exists an algorithm which takes as input a description of a semialgebraic subset $S \subset \mathbb {R}^k$ given by a quantifier-free first-order formula $\phi $ in the language of the reals and produces as output a simplicial complex $\Delta $ , whose geometric realization, $|\Delta |$ is $\ell $ -equivalent to S. The complexity of our algorithm is bounded by $(sd)^{k^{O(\ell )}}$ , where s is the number of polynomials appearing in the formula $\phi $ , and d a bound on their degrees. For fixed $\ell $ , this bound is singly exponential in k. In particular, since $\ell $ -equivalence implies that the homotopy groups up to dimension $\ell $ of $|\Delta |$ are isomorphic to those of S, we obtain a reduction (having singly exponential complexity) of the problem of computing the first $\ell $ homotopy groups of S to the combinatorial problem of computing the first $\ell $ homotopy groups of a finite simplicial complex of size bounded by $(sd)^{k^{O(\ell )}}$ .

Design and Verification of Petri-Net-Based Cyber-Physical Systems Oriented toward Implementation in Field-Programmable Gate Arrays—A Case Study Example

This paper presents a novel design approach of a Petri-net-based cyber-physical system (CPS). The idea is oriented toward implementation in a field-programmable gate array (FPGA). The proposed technique permits error detection in the system at the early specification stage in order to reduce the time and prototyping cost of the CPS. Due to the state explosion problem, the traditional verification methods have exponential computational complexity. In contrast, we show that under certain assumptions, the proposed algorithm is able to detect possible errors in the system even in cubic O(|T|2|P|) time. Furthermore, all the required steps of the proposed design method are presented and discussed. The idea is illustrated by a real-life case study example of a traffic light crossroad. The system was modelled, analysed, implemented, and finally validated within the FPGA device (Virtex-5 family).

The Polynomial Algorithm of Finding the Shortest Path in a Divisible Multiple Graph

In this paper, we study undirected multiple graphs of any natural multiplicity к &gt; 1. There are edges of three types: ordinary edges, multiple edges and multi-edges. Each edge of the last two types is a union of к linked edges, which connect 2 or (к + 1) vertices, correspondingly. The linked edges should be used simultaneously. If a vertex is incident to a multiple edge, it can be also incident to other multiple edges and it can be the common end of к linked edges of some multi-edge. If a vertex is the common end of some multi-edge, it cannot be the common end of another multi-edge. Divisible multiple graphs are characterized by a possibility to divide the graph into к parts, which are adjusted on the linked edges and which have no common edges. Each part is an ordinary graph. As for an ordinary graph, we can define the integer function of the length of an edge for a multiple graph and set the problem of the shortest path joining two vertices. Any multiple path is a union of к ordinary paths, which are adjusted on the linked edges of all multiple and multi-edges. In the article, we show that the problem of the shortest path is polynomial for a divisible multiple graph. The corresponding polynomial algorithm is formulated. Also we suggest the modification of the algorithm for the case of an arbitrary multiple graph. This modification has an exponential complexity in the parameter к.

Dispatching Arrays with Tasks of Equal Resource Measure in GRID Systems

The role of computing and time resource management of parallel systems when dispatching multiprocessor tasks increases significantly in Grid systems consisting of multiple sites with multiprocessor computing systems, with multisite execution of a parallel task on several sites simultaneously. Such Grid systems of centralized architecture are modeled by the resource quadrant. User's request for maintenance by the Grid system dispatcher is modeled by a resource rectangle with horizontal and vertical dimensions, respectively, equal to the number of time and processor resource units required to fulfill the request. Examples of the exponential complexity of dispatching resource rectangles are the stacking of consecutive resource squares and consecutive resource rectangles of equal perimeter into an enclosing rectangle of the minimum area. Heuristic algorithms of polynomial labor intensity based on the operations of dynamic integration of resource rectangles in the environment of resource rectangles are of practical value. The quality of dispatching is assessed by a non-Euclidean heuristic measure that takes into account the area and shape of the occupied resource area. The quality of dispatching arrays with requests of the same resource measure equal to the product of the number of required processors and runtime is analyzed. In this paper, the quality of three polynomial level algorithms in height and three polynomial level algorithms in length (with the nearest approach to the level, with exceeding of the level and with minimum deviation) is evaluated when dispatching arrays with requests of equal resource measure. Such arrays belong to the parabolic quadratic type and contain user's tasks of circular, hyperbolic and parabolic type. On five test arrays, it is shown that H-finite-level algorithms with a with the nearest approach to the level and with minimum deviation have the smallest value of the maximum of the heuristic measure of 8.45. When servicing arrays with user's tasks of the same resource measure in Grid systems, it is recommended to use the polynomial Н- finite-level algorithm in length with the nearest approach to the level which is introduced in this paper.

A Novel Control-Theory-Based Approach to Scheduling of High-Throughput Screening System for Enzymatic Assay

Nowadays, high-throughput screening (HTS) systems are widely used in pharmaceutical industries and laboratories for the discovery of new drugs and biomedical substances. It is important to efficiently schedule them so as to reduce the cost. In the operation of an HTS system, a microplate may visit some resources more than once and complex time window constraints are imposed on some activities and activity sequences. Moreover, with the consistency requirement, a one-microplate cyclic schedule is necessary. Thus, its scheduling problem is very challenging. This article studies the scheduling problem of an HTS system for an enzymatic assay, a typical application of HTSs, from the perspective of control theory. The system is modeled by resource-oriented Petri nets (ROPNs). With the model, necessary and sufficient conditions under which a feasible cyclic schedule exists are established. Then, we determine how many microplates should be in the system for concurrent processing and the transition firing sequence to obtain the activity sequence for an optimal and feasible schedule. In this way, a feasible and optimal cyclic schedule can be found by very simple computations, which shows that polynomial algorithms for an optimal schedule exist, while the existing studies apply mathematical programming with exponential computation complexity. Also, its efficient implementation is given.

N-body correlation of Tonks–Girardeau gas

For the well-known exponential complexity it is a giant challenge to calculate the correlation function for general many-body wave function. We investigate the ground state $n$th-order correlation functions of the Tonks-Girardeau (TG) gases. Basing on the wavefunction of free fermions and Bose-Fermi mapping method we obtain the exact ground state wavefunction of TG gases. Utilizing the properties of Vandermonde determinant and Toeplitz matrix, the $n$th-order correlation function is formulated as $(N-n)$-order Toeplitz determinant, whose element is the integral dependent on 2$(N-n)$ sign functions and can be computed analytically. By reducing the integral on domain $[0,2\pi]$ into the summation of the integral on several independent domains, we obtain the explicit form of the Toeplitz matrix element ultimately. As the applications we deduce the concise formula of the reduced two-body density matrix and discuss its properties. The corresponding natural orbitals and their occupation distribution are plotted. Furthermore, we give a concise formula of the reduced three-body density matrix and discuss its properties. It is shown that in the successive second measurements, atoms appear in the regions where atoms populate with the maximum probability in the first measurement.

End Users' and Other Stakeholders' Needs and Requirements in the Development of a Personalized Integrated Care Platform (PROCare4Life) for Older People With Dementia or Parkinson Disease: Mixed Methods Study.

With what has been known as the "triple-win effect", introducing information and communication technologies (ICTs) in the health care of neurodegenerative diseases is beneficial in delaying the need for institutional care, reducing the associated health care costs, reducing the caregiving burden, and improving individuals' quality of life. Nevertheless, the mismatch between the users' expectations and their actual needs remains one of the main challenges that can reduce the usability of technology solutions. Therefore, the European project Personalized Integrated Care Promoting Quality of Life for Older People (PROCare4Life), which aimed to develop an ICT-based platform for all parties involved in the health care of neurodegenerative diseases, adopted a user-centered design approach, where all users are involved from the inception and throughout the platform development and implementation to integrate their needs and requirements in the proposed platform. This paper presents the results of a study on the needs and requirements of the potential end users (older people with neurodegenerative diseases, caregivers, and health care professionals) and other key stakeholders in the development of the PROCare4Life platform. A mixed qualitative and quantitative study design was used, including 2 web-based surveys, 40 interviews, and 4 workshops. The study was conducted between April and September 2020 in 5 European countries: Germany, Italy, Portugal, Romania, and Spain. Both data types were analyzed separately and then merged and interpreted, with greater priority placed on qualitative research. A total of 217 participants were recruited; 157 (72.4%) of them completed the web-based surveys (n=85, 54.1% patients and n=72, 45.9% caregivers), and 60 (27.6%) individuals participated in the qualitative research (20/60, 33% health care professionals; 5/60, 8% patients; 5/60, 8% caregivers; and 30/60, 50% key stakeholders). We identified 3 main themes (T): (T1) experiences associated with illness, (T2) thoughts about the platform technology, and (T3) desired properties. Alerts for adverse events, communication tools, reminders, and monitoring are constantly needed functionalities, whereas ease of use, personalization, and user-friendliness are foreseen as necessary features. This paper identified the key personal, social, and health factors that influence the daily lives of the potential end users and reflected on their needs and expectations regarding the design of the proposed PROCare4Life platform. The collected data were useful for the development of the PROCare4Life platform. Although the combination and collection of features for diverse user groups are typical for integrated care platforms, it results in exponential complexity for designers, developers, and users. Contradicting opinions and several concerns in this study demonstrate that an ICT-integrated care platform should not promise too much for too many. Instead, selection, focus, and, sometimes, restriction to essentials are necessary. Users and other stakeholders should be involved in these decisions. RR2-10.2196/22463.

A New Four-Dimensional Chaotic System with Multistability and Its Predefined-Time Synchronization

A new chaotic system is obtained by modifying the Sprott-C system. Then the phase diagrams, power spectra, 0–1 tests, Poincaré maps, Lyapunov exponential spectra, time sequences, and complexity are studied. Research indicates that the system is sensitive to parameters and initial conditions, and bursting oscillation, transient chaos and multistability are investigated. The complexity of the new system is calculated using the Sample Entropy (SE) complexity algorithm, including selecting more suitable initial values and parameters for the application. In addition, the system circuit designed by Multisim and the actual digital circuit realized by Field Programmable Gate Array (FPGA) verify the feasibility of the system. Finally, to obtain a more appropriate synchronization result for practical applications, a synchronous controller is designed to successfully implement the predefined-time synchronization of the system in different dimensions. The simulation results demonstrate that the predefined-time synchronization can control the synchronous time and is unaffected by the initial conditions. The results demonstrate that this synchronization method is well accommodated to practical applications.

Sub-6 GHz V2X-Assisted Synchronous Millimeter Wave Scheduler for Vehicle-to-Vehicle Communications

As millimeter wave (mmWave) technology becomes more integrated into today's communication infrastructure, its application to mobile scenarios has attracted considerable interests. In particular, mmWave technology is one of the leading candidates in Vehicle-to-Everything (V2X) community to address the ever-rising data exchange demand from vehicles. However, the inherent directionality of the technology poses challenges to peer discovery and transmission scheduling in typical V2X scenarios, causing significant loss of network capacity. To mitigate this issue, we propose a novel sub-6 GHz V2X-assisted synchronous mmWave communication scheduler in this paper. The sub-6 GHz channel serves as control channel for mmWave scheduling. The scheduler carefully considers data importance and freshness in determining communication schedule, such that network utility across mmWave links is maximized. We formulate the scheduling problem into an integer linear programming (ILP) problem. However, ILP problem is NP-hard and has exponential computational complexity for the worst cases. We then develop a scheduling algorithm, maximum weight matching based iterative algorithm (MWMIA), that operates in polynomial time with performance guarantees for the NP-hard ILP, by leveraging structural properties of link conflicts. Comparative simulation studies verify the effectiveness of our scheduler against other solutions.