Minimizing the maximal weighted lateness of delivering orders between two railroad stations

We consider the planning problem for freight transportation between two railroad stations. We are required to fulfill orders (transport cars by trains) that arrive at arbitrary time moments and have different value (weight). The speed of trains moving between stations may be different. We consider problem settings with both fixed and undefined departure times for the trains. For the problem with fixed train departure times we propose an algorithm for minimizing the weighted lateness of orders with time complexity O(qn ² log n) operations, where q is the number of trains and n is the number of orders. For the problem with undefined train departure and arrival times we construct a Pareto optimal set of schedules optimal with respect to criteria wL _max and C _max in O(n ² max{n log n, q log v}) operations, where v is the number of time windows during which the trains can depart. The proposed algorithm allows to minimize both weighted lateness wL _max and total time of fulfilling freight delivery orders C _max.     

The formula of the solution for some classes of initial boundary value problems for the hyperbolic equation with two independent variables

A new representation is proved of the solutions of initial boundary value problems for the equation of the form u _xx (x, t) + r(x)u _x (x, t) ? q(x)u(x, t) = u _tt (x, t) + μ(x)u _t (x, t) in the section (under boundary conditions of the 1st, 2nd, or 3rd type in any combination). This representation has the form of the Riemann integral dependent on the x and t over the given section.     

Continuity of the Effective Delay Operator for Networks Based on the Link Delay Model

This paper is concerned with a dynamic traffic network performance model, known as dynamic network loading (DNL), that is frequently employed in the modeling and computation of analytical dynamic user equilibrium (DUE). As a key component of continuous-time DUE models, DNL aims at describing and predicting the spatial-temporal evolution of traffic flows on a network that is consistent with established route and departure time choices of travelers, by introducing appropriate dynamics to flow propagation, flow conservation, and travel delays. The DNL procedure gives rise to the path delay operator, which associates a vector of path flows (path departure rates) with the corresponding path travel costs. In this paper, we establish strong continuity of the path delay operator for networks whose arc flows are described by the link delay model (Friesz et al., Oper Res 41(1):80–91, 1993; Carey, Networks and Spatial Economics 1(3):349–375, 2001). Unlike the result established in Zhu and Marcotte (Transp Sci 34(4):402–414, 2000), our continuity proof is constructed without assuming a priori uniform boundedness of the path flows. Such a more general continuity result has a few important implications to the existence of simultaneous route-and-departure-time DUE without a priori boundedness of path flows, and to any numerical algorithm that allows convergence to be rigorously analyzed.     

On the Smallest Size of an Almost Complete Subset of a Conic in PG(2, <Emphasis Type="Italic">q</Emphasis>) and Extendability of Reed–Solomon Codes

Abstract—In the projective plane PG(2, q), a subset S of a conic C is said to be almost complete if it can be extended to a larger arc in PG(2, q) only by the points of C \ S and by the nucleus of C when q is even. We obtain new upper bounds on the smallest size t(q) of an almost complete subset of a conic, in particular,

$$t(q) < \sqrt {q(3lnq + lnlnq + ln3)} + \sqrt {\frac{q}{{3\ln q}}} + 4 \sim \sqrt {3q\ln q} ,t(q) < 1.835\sqrt {q\ln q.} $$

The new bounds are used to extend the set of pairs (N, q) for which it is proved that every normal rational curve in the projective space PG(N, q) is a complete (q+1)-arc, or equivalently, that no [q+1,N+1, q?N+1]_q generalized doubly-extended Reed–Solomon code can be extended to a [q + 2,N + 1, q ? N + 2]_q maximum distance separable code.

     

Exact and approximate flexible aggregate similarity search

Aggregate similarity search, also known as aggregate nearest-neighbor (Ann) query, finds many useful applications in spatial and multimedia databases. Given a group Q of M query objects, it retrieves from a database the objects most similar to Q, where the similarity is an aggregation (e.g., \({{\mathrm{sum}}}\), \(\max \)) of the distances between each retrieved object p and all the objects in Q. In this paper, we propose an added flexibility to the query definition, where the similarity is an aggregation over the distances between p and any subset of \(\phi M\) objects in Q for some support \(0< \phi \le 1\). We call this new definition flexible aggregate similarity search and accordingly refer to a query as a flexible aggregate nearest-neighbor ( Fann ) query. We present algorithms for answering Fann queries exactly and approximately. Our approximation algorithms are especially appealing, which are simple, highly efficient, and work well in both low and high dimensions. They also return near-optimal answers with guaranteed constant-factor approximations in any dimensions. Extensive experiments on large real and synthetic datasets from 2 to 74 dimensions have demonstrated their superior efficiency and high quality.     

Polylogarithms and the Asymptotic Formula for the Moments of Lebesgue’s Singular Function

Recall that Lebesgue’s singular function L(t) is defined as the unique solution to the equation L(t) = qL(2t) + pL(2t ? 1), where p, q > 0, q = 1 ? p, p ≠ q. The variables M _n = ∫₀¹t ⁿ dL(t), n = 0,1,… are called the moments of the function The principal result of this work is \({M_n} = {n^{{{\log }_2}p}}{e^{ - \tau (n)}}(1 + O({n^{ - 0.99}}))\), where the function τ(x) is periodic in log₂x with the period 1 and is given as \(\tau (x) = \frac{1}{2}1np + \Gamma '(1)lo{g_2}p + \frac{1}{{1n2}}\frac{\partial }{{\partial z}}L{i_z}( - \frac{q}{p}){|_{z = 1}} + \frac{1}{{1n2}}\sum\nolimits_{k \ne 0} {\Gamma ({z_k})L{i_{{z_k} + 1}}( - \frac{q}{p})} {x^{ - {z_k}}}\), \({z_k} = \frac{{2\pi ik}}{{1n2}}\), k ≠ 0. The proof is based on poissonization and the Mellin transform.     

Monochromatic and bichromatic ranked reverse boolean spatial keyword nearest neighbors search

Recently, Reverse k Nearest Neighbors (RkNN) queries, returning every answer for which the query is one of its k nearest neighbors, have been extensively studied on the database research community. But the RkNN query cannot retrieve spatio-textual objects which are described by their spatial location and a set of keywords. Therefore, researchers proposed a RSTkNN query to find these objects, taking both spatial and textual similarity into consideration. However, the RSTkNN query cannot control the size of answer set and to be sorted according to the degree of influence on the query. In this paper, we propose a new problem Ranked Reverse Boolean Spatial Keyword Nearest Neighbors query called Ranked-RBSKNN query, which considers both spatial similarity and textual relevance, and returns t answers with most degree of influence. We propose a separate index and a hybrid index to process such queries efficiently. Experimental results on different real-world and synthetic datasets show that our approaches achieve better performance.     

Reverse Furthest Neighbors Query in Road Networks

Given a road network G = (V,E), where V (E) denotes the set of vertices(edges) in G, a set of points of interest P and a query point q residing in G, the reverse furthest neighbors (Rfn _R ) query in road networks fetches a set of points p ∈ P that take q as their furthest neighbor compared with all points in P ∪ {q}. This is the monochromatic Rfn _R (Mrfn _R ) query. Another interesting version of Rfn _R query is the bichromatic reverse furthest neighbor (Brfn _R ) query. Given two sets of points P and Q, and a query point q ∈ Q, a Brfn _R query fetches a set of points p ∈ P that take q as their furthest neighbor compared with all points in Q. This paper presents efficient algorithms for both Mrfn _R and Brfn _R queries, which utilize landmarks and partitioning-based techniques. Experiments on real datasets confirm the efficiency and scalability of proposed algorithms.     

Optimal Path Embedding in the Exchanged Crossed Cube

The (s + t + 1)-dimensional exchanged crossed cube, denoted as ECQ(s, t), combines the strong points of the exchanged hypercube and the crossed cube. It has been proven that ECQ(s, t) has more attractive properties than other variations of the fundamental hypercube in terms of fewer edges, lower cost factor and smaller diameter. In this paper, we study the embedding of paths of distinct lengths between any two different vertices in ECQ(s, t). We prove the result in ECQ(s, t): if s ≥ 3, t ≥ 3, for any two different vertices, all paths whose lengths are between \( \max \left\{9,\left\lceil \frac{s+1}{2}\right\rceil +\left\lceil \frac{t+1}{2}\right\rceil +4\right\} \) and 2 ^s+t+1 ? 1 can be embedded between the two vertices with dilation 1. Note that the diameter of ECQ(s, t) is \( \left\lceil \frac{s+1}{2}\right\rceil +\left\lceil \frac{t+1}{2}\right\rceil +2 \). The obtained result is optimal in the sense that the dilations of path embeddings are all 1. The result reveals the fact that ECQ(s, t) preserves the path embedding capability to a large extent, while it only has about one half edges of CQ _n .     

Finding maximal ranges with unique topics in a text database

Recent years have witnessed the rapid growth of text data, and thus the increasing importance of in-depth analysis of text data for various applications. Text data are often organized in a database with documents labeled by attributes like time and location. Different documents manifest different topics. The topics of the documents may change along the attributes of the documents, and such changes have been the subject of research in the past. However, previous analyses techniques, such as topic detection and tracking, topic lifetime, and burstiness, all focus on the topic behavior of the documents in a given attribute range without contrasting to the documents in the overall range. This paper introduces the concept of u n i q u e t o p i c s, referring to those topics that only appear frequently within a small range of documents but not in the whole range. These unique topics may reflect some unique characteristics of documents in this small range not found outside of the range. The paper aims at an efficient pruning-based algorithm that, for a user-given set of keywords and a user-given attribute, finds the maximal ranges along the given attribute and their unique topics that are highly related to the given keyword set. Thorough experiments show that the algorithm is effective in various scenarios.     

On the Number of Edges of a Uniform Hypergraph with a Range of Allowed Intersections

We study the quantity p(n, k, t₁, t₂) equal to the maximum number of edges in a k-uniform hypergraph having the property that all cardinalities of pairwise intersections of edges lie in the interval [t₁, t₂]. We present previously known upper and lower bounds on this quantity and analyze their interrelations. We obtain new bounds on p(n, k, t₁, t₂) and consider their possible applications in combinatorial geometry problems. For some values of the parameters we explicitly evaluate the quantity in question. We also give a new bound on the size of a constant-weight error-correcting code.     

Modeling Mode and Route Similarities in Network Equilibrium Problem with Go-Green Modes

Environmental sustainability is a common requirement on the development of various real-world systems, especially on road transportation systems. Motorized vehicles generate a large amount of harmful emissions, which have adverse effects to the environment and human health. Environmental sustainability requires more promotions of ‘go-green’ transportation modes such as public transit and bicycle to realize the increasing travel demands while keeping the environmental expenses low. In this paper, we make use of recent advances in discrete choice modeling to develop equivalent mathematical programming formulations for the combined modal split and traffic assignment (CMSTA) problem that explicitly considers mode and route similarities under congested networks. Specifically, a nested logit model is adopted to model the modal split problem by accounting for mode similarity among the available modes, and a cross-nested logit model is used to account for route overlapping in the traffic assignment problem. This new CMSTA model has the potential to enhance the behavioral modeling of travelers’ mode shift between private motorized mode and ‘go-green’ modes as well as their mode-specific route choices, and to assist in quantitatively evaluating the effectiveness of different ‘go-green’ promotion policies.     

Efficient hierarchical identity based encryption scheme in the standard model over lattices

Using lattice basis delegation in a fixed dimension, we propose an efficient lattice-based hierarchical identity based encryption (HIBE) scheme in the standard model whose public key size is only (dm² + mn) log q bits and whose message-ciphertext expansion factor is only log q, where d is the maximum hierarchical depth and (n, m, q) are public parameters. In our construction, a novel public key assignment rule is used to averagely assign one random and public matrix to two identity bits, which implies that d random public matrices are enough to build the proposed HIBE scheme in the standard model, compared with the case in which 2d such public matrices are needed in the scheme proposed at Crypto 2010 whose public key size is (2dm² + mn +m) log q. To reduce the message-ciphertext expansion factor of the proposed scheme to log q, the encryption algorithm of this scheme is built based on Gentry’s encryption scheme, by which m² bits of plaintext are encrypted into m² log q bits of ciphertext by a one time encryption operation. Hence, the presented scheme has some advantages with respect to not only the public key size but also the message-ciphertext expansion factor. Based on the hardness of the learning with errors problem, we demonstrate that the scheme is secure under selective identity and chosen plaintext attacks.     

Asymptotic bounds for the rate of colored superimposed codes

We introduce the notion of a q-ary (r ₀, r ₁, ..., r _q?1) superimposed code. We obtain upper and lower asymptotic bounds for the rate of these (colored) codes.     

Integrating tourist packages and tourist attractions for personalized trip planning based on travel constraints

In recent years, with the upgrading of mobile positioning and the popularity of smart devices, location related research gets a lot of attentions. One of popular issues is the trip planning problem. Although many related scientific or technical literature have been proposed, most of them focused only on tourist attraction recommendation or arrangement meeting some user demands. In fact, to grasp the huge tourism opportunities, more and more tour operators design tourist packages and provide to users. Generally, tourist packages have many advantages such as cheaper ticket price and higher transportation convenience. However, researches on trip planning combining tourist packages have not been mentioned in the past studies. In this research, we present a new approach named Package-Attraction-based Trip Planner (PAT-Planner) to simultaneously combine tourist packages and tourist attractions for personalized trip planning satisfying users’ travel constraints. In PAT-Planner, we first based on user preferences and temporal characteristics to design a Score Inference Model for respectively measuring the score of a tourist package or tourist attraction. Then, we develop the Hybrid Trip-Mine algorithm meeting user travel constraints for personalized trip planning. Besides, we further propose two improvement strategies, namely Score Estimation and Score Bound Tightening, based on Hybrid Trip-Mine to speed up the trip planning efficiency. As far as we know, our study is the first attempt to simultaneously combine tourist packages and tourist attractions on trip planning problem. Through a series of experimental evaluations and case studies using the collected Gowalla datasets, PAT-Planner demonstrates excellent planning effects.     

Symmetric Masks for In-fill Pixel Interpolation on Discrete <Emphasis Type="Italic">p</Emphasis>:<Emphasis Type="Italic">q</Emphasis> Lattices

A 2D p:q lattice contains image intensity entries at pixels located at regular, staggered intervals that are spaced p rows and q columns apart. Zero values appear at all other intermediate grid locations. We consider here the construction, for any given p:q, of convolution masks to smoothly and uniformly interpolate values across all of the intermediate grid positions. The conventional pixel-filling approach is to allocate intensities proportional to the fractional area that each grid pixel occupies inside the boundaries formed by the p:q lines. However, these area-based masks have asymmetric boundaries, flat interior values and may be odd or even in size. Where edges, lines or points are in-filled, area-based p:q masks imprint intensity patterns that recall p:q because the shape of those masks is asymmetric and depends on p:q. We aim to remove these “memory” artefacts by building symmetric p:q masks. We show here that smoother, symmetric versions of such convolution masks exist. The coefficients of the masks constructed here have simple integer values whose distribution is derived purely from symmetry considerations. We have application for these symmetric interpolation masks as part of a precise image rotation algorithm which disguises the rotation angle, as well as to smooth back-projected values when performing discrete tomographic image reconstruction.     

On <Emphasis Type="Italic">m</Emphasis>-Near-Resolvable Block Designs and <Emphasis Type="Italic">q</Emphasis>-ary Constant-Weight Codes

We introduce m-near-resolvable block designs. We establish a correspondence between such block designs and a subclass of (optimal equidistant) q-ary constant-weight codes meeting the Johnson bound. We present constructions of m-near-resolvable block designs, in particular based on Steiner systems and super-simple t-designs.     

<Emphasis Type="Italic">α</Emphasis>-Systems of differential inclusions and their unification

This paper introduces α-systems of differential inclusions on a bounded time interval [t₀, ?] and defines α-weakly invariant sets in [t₀, ?] × ?_n, where ?_n is a phase space of the differential inclusions. We study the problems connected with bringing the motions (trajectories) of the differential inclusions from an α-system to a given compact set M ? ?_n at the moment ? (the approach problems). The issues of extracting the solvability set W ? [t₀, ?] × ?ⁿ in the problem of bringing the motions of an α-system to M and the issues of calculating the maximal α-weakly invariant set W^c ? [t₀, ?] × ?ⁿ are also discussed. The notion of the quasi-Hamiltonian of an α-system (α-Hamiltonian) is proposed, which seems important for the problems of bringing the motions of the α-system to M.     

Diverse nearest neighbors queries using linear skylines

k-nearest neighbor (k-NN) queries are well-known and widely used in a plethora of applications. However, in the original definition of k-NN queries there is no concern regarding diversity of the answer set with respect to the user’s interests. For instance, travelers may be looking for touristic sites that are close to where they are, but that would also lead them to see different parts of the city. Likewise, if one is looking for restaurants close by, it may be more interesting to learn about restaurants of different categories or ethnicities which are nonetheless relatively close. The interesting novel aspect of this type of query is that there are two competing criteria to be optimized: closeness and diversity. We propose two approaches that leverage the notion of linear skyline queries in order to find the k diverse nearest neighbors within a radius r from a given query point, or (k, r)-DNNs for short. Our proposed approaches return a relatively small set containing all optimal solutions for any linear combination of the weights a user could give to the two competing criteria, and we consider three different notions of diversity: spatial, categorical and angular. Our experiments, varying a number of parameters and exploring synthetic and real datasets, in both Euclidean space and road networks, respectively, show that our approaches are several orders of magnitude faster than a straightforward approach.     

Threshold quantum secret sharing based on single qubit

Based on unitary phase shift operation on single qubit in association with Shamir’s (t, n) secret sharing, a (t, n) threshold quantum secret sharing scheme (or (t, n)-QSS) is proposed to share both classical information and quantum states. The scheme uses decoy photons to prevent eavesdropping and employs the secret in Shamir’s scheme as the private value to guarantee the correctness of secret reconstruction. Analyses show it is resistant to typical intercept-and-resend attack, entangle-and-measure attack and participant attacks such as entanglement swapping attack. Moreover, it is easier to realize in physic and more practical in applications when compared with related ones. By the method in our scheme, new (t, n)-QSS schemes can be easily constructed using other classical (t, n) secret sharing.