Recent years have witnessed a growing trend in the utilization of Electric Vehicles (EVs), however with the increased usage of EVs, appropriate strategies for supporting the charging demands has not garnered much attention. The absence of adaptable plans in charging may result in minimized participation; further, the charging demands have to be addressed with utmost care for ensuring reliability and

Given a configuration of pebbles on the vertices of a graph G, a pebbling move removes two pebbles from a vertex and puts one pebble on an adjacent vertex. The pebbling number of a graph G is the smallest number of pebbles required such that, given an arbitrary initial configuration of pebbles, one pebble can be moved to any vertex of G through some sequence of pebbling moves. Through constructing

We propose an analytical definition of discrete circles in the hexagonal grid. Our approach is based on a non-constant thickness function. We determine the thickness using the (edge and vertex) flake model. Both types of circles are connected. We prove that edge flake circles are without simple points for integer radii. Incremental generation algorithms are deduced from the analytical characterization

In this work, we consider a combinatorial optimization problem with direct applications in blockchain mining, namely finding the most lucrative blocks for Bitcoin miners, and propose optimal algorithmic solutions. Our experiments show that our algorithms increase the miners’ revenues by more than a million dollars per month. Modern blockchains reward their miners in two ways: (i) a base reward for

The vectorial nonlinearity of a vector-valued function is its distance from the set of affine functions. In 2017, Liu, Mesnager, and Chen conjectured a general upper bound for the vectorial linearity. Recently, Carlet established a lower bound in terms of differential uniformity. In this paper, we improve Carlet's lower bound. Our approach is based on the fact that the level sets of a vectorial Boolean

Facial expression-based Emotion Recognition (FER) is crucial in human–computer interaction and affective computing, particularly when addressing diverse age groups. This paper introduces the Multi-Scale Vision Transformer with Contrastive Learning (MViT-CnG), an age-adaptive FER approach designed to enhance the accuracy and interpretability of emotion recognition models across different classes. The

This paper studies the online multiple time series search problem with interrelated prices (MTSS-ip). This perspective narrows the distance between the problem and the reality of market prices with limited variation. In MTSS-ip, the products arrive periodically, and the decision maker has a limited storage size without knowing future prices. The prices of two adjacent periods are interrelated. This

This paper introduces the concepts of spectral influence and spectral cyclicality, both derived from the largest eigenvalue of a graph’s adjacency matrix. These two novel centrality measures capture both diffusion and interdependence from a local and global perspective respectively. We propose a new clustering algorithm that identifies communities with high cyclicality and interdependence, allowing

A subset \( S\subseteq V(G) \), where V(G) is the vertex set of a graph G, is a disjunctive total dominating set of G if each vertex has a neighbour in S or has at least two vertices in S at distance two from it. The minimum cardinality of such a set is the disjunctive total domination number. There are some graph modifications on the edge or vertex of a graph, one of which is subdividing an edge.

Graph edit distance is usually used for graph similarity checking due to its low information loss and flexibility advantages. However, graph edit distance can’t be used efficiently because it is an NP-Hard problem. Many graph edit distance heuristic algorithms have been proposed to solve this problem. However, some heuristic algorithms for generating \(walk\) generate unnecessary sequences because

The selfish bin packing with partial punishment is studied in this paper. In this problem, the utility of an item is defined as the load of the bin it is in. Each item plays the role of a selfish agent and wants to maximize its own utility. If an item with size \(s_i\) moves to another bin, it has to pay the partial punishment of \(\alpha s_{i}\), where \(0<\alpha <1\). We prove that the price of anarchy

Customer segmentation, a critical strategy in marketing, involves grouping consumers based on shared characteristics like age, income, and geographical location, enabling firms to effectively establish different strategies depending on the target group of customers. Clustering is a widely utilized data analysis technique that facilitates the identification of diverse groups, each distinguished by their

In this paper we study the online over-time scheduling on an unbounded parallel-batch machine to minimize the weighted makespan. First, we show that the general problem has a low bound 2 and then design a 4-competitive online algorithm. Furthermore, we consider a special case in which the jobs have agreeable processing times and weights. When all jobs have the same weights (the task is to minimize

In this paper, we theoretically study the Combinatorial Multi-Armed Bandit problem with stochastic monotone k-submodular reward function under full-bandit feedback. In this setting, the decision-maker is allowed to select a super arm composed of multiple base arms in each round and then receives its k-submodular reward. The k-submodularity enriches the application scenarios of the problem we consider

In this paper, we present approximation algorithms for the Airport and Railway problem (AR) on several classes of graphs. The \(\text{ AR }\) problem, introduced as reported by Adamaszek et al. (in: Ollinger, Vollmer (eds) 33rd symposium on theoretical aspects of computer science (STACS 2016). Leibniz international proceedings in informatics (LIPIcs), Dagstuhl, 2016), is a combination of the Capacitated

With the rapid development of network architectures and application technologies, there is an increasing number of latency-sensitive tasks generated by user devices, necessitating real-time processing on edge servers. During peak periods, user devices compete for limited edge resources to execute their tasks, while different edge servers also compete for transaction opportunities. This article focus

Let (G,+,0) be a finite abelian group and let ηN(G) be the smallest integer ℓ such that every sequence over G∖{0} of length ℓ has two joint short minimal zero-sum subsequences. In 2013, Gao et al. obtained that ηN(Cn⊕Cn)=3n+1 for every n≥2 and solved the corresponding inverse problem for groups Cp⊕Cp, where p is a prime. In this paper, we determine the precise value of ηN(G) for all finite abelian

Transmit a codeword ▪, that belongs to an (ℓ−1)-deletion-correcting code of length n, over a t-deletion channel for some 1≤ℓ≤t

In this paper, we provide a complete classification of 2-(v,k,2) designs admitting a flag-transitive automorphism group of affine type with the only exception of the semilinear 1-dimensional group. Alongside this analysis, we provide a construction of seven new families of such flag-transitive 2-designs, one of them infinite, and some of them involving remarkable objects such as t-spreads, translation

Let Dn be the set of partitions of n into distinct parts, and srp(λ) be the sum of reciprocals of the parts of the partition λ. We show that as n→∞,E[srp(λ):λ∈Dn]∼log⁡(3n)4andVar[srp(λ):λ∈Dn]∼π224. Moreover, for Pn, the set of ordinary partitions of n, we show that as n→∞,E[srp(λ):λ∈Pn]∼πn6andVar[srp(λ):λ∈Pn]∼π215n. To prove these asymptotic formulas in a uniform manner, we derive a general asymptotic

Two families A and B are cross-intersecting if A∩B≠∅ for any A∈A and B∈B. We call t families A1,A2,…,At pairwise cross-intersecting families if Ai and Aj are cross-intersecting for 1≤i

In this work, we consider the Submodular Maximization under Knapsack (\(\textsf{SMK}\)) constraint problem over the ground set of size n. The problem recently attracted a lot of attention due to its applications in various domains of combinatorial optimization, artificial intelligence, and machine learning. We improve the approximation factor of the fastest deterministic algorithm from \(6+\epsilon

We show that the dominance complex D(G) of a graph G coincides with the combinatorial Alexander dual of the neighborhood complex N(G‾) of the complement of G. Using this, we obtain a relation between the chromatic number χ(G) of G and the homology group of D(G). We also obtain several known results related to dominance complexes from well-known facts of neighborhood complexes. After that, we suggest

This paper studies a due-window assignment scheduling problem with deterioration effects on a single-machine. Under different due-window assignment, i.e., the due-window of a job without any restriction, our goal is to make a decision on the optimal due-window and sequence of all jobs to minimize the weighted sum of earliness and tardiness, number of early and delayed, due-window starting time and

The neighbor-connectivity of a graph G, denoted by \(\kappa _{NB}(G)\), is the least number of vertices such that removing their closed neighborhoods from G results in a graph that is empty, complete, or disconnected. In the paper, we show that for any graph G of order n, \(\kappa _{NB}(G)\le \lceil \sqrt{2n}\ \rceil -2\). We pose a conjecture that \(\kappa _{NB}(G)\le \lceil \sqrt{n}\ \rceil -1\)

In the field of optimization algorithms, nature-inspired techniques have garnered attention for their adaptability and problem-solving prowess. This research introduces the Arctic Fox Algorithm (AFA), an innovative optimization technique inspired by the adaptive survival strategies of the Arctic fox, designed to excel in dynamic and complex optimization landscapes. Incorporating gradient flow dynamics

In order to maximize full-view coverage of moving targets in Camera Sensor Networks (CSNs), a novel method known as “group set cover” is presented in this research. Choosing the best camera angles and placements to accomplish full-view coverage of the moving targets is one of the main focuses of the research in CSNs. Discretize the target into multiple views of [0, 2\(\pi \)], use a set of views of

The assumption of independent subvectors arises in many aspects of multivariate analysis. In most real-world applications, however, we lack prior knowledge about the number of subvectors and the sp...

Motivated by a classical result of Graver and Jurkat (1973) and Graham, Li, and Li (1980) in combinatorial design theory, which states that the permutations of t-(v,k) minimal trades generate the vector space of all t-(v,k) trades, we investigate the vector space spanned by permutations of an arbitrary trade. We prove that this vector space possesses a decomposition as a direct sum of subspaces formed

We use techniques from algebraic and extremal combinatorics to derive upper bounds on the number of independent sets in several (hyper)graphs arising from finite geometry. In this way, we obtain asymptotically sharp upper bounds for partial ovoids and EKR-sets of flags in polar spaces, line spreads in PG(2r−1,q) and plane spreads in PG(5,q), and caps in PG(3,q). The latter result extends work due to

We investigate the minimum number of cycles of specified lengths in planar n-vertex triangulations G. We prove that this number is Ω(n) for any cycle length at most 3+max⁡{rad(G⁎),⌈(n−32)log3⁡2⌉}, where rad(G⁎) denotes the radius of the triangulation's dual, which is at least logarithmic but can be linear in the order of the triangulation. We also show that there exist planar hamiltonian n-vertex triangulations

In 2012, Andrews and Merca proved a truncated theorem on Euler's pentagonal number theorem. Since then, a number of results on truncated theta series have been proved. In this paper, we find the connections between truncated sums of certain partition functions and the minimal excludant statistic which has been found to exhibit connections with a handful of objects such as Dyson's crank. We present

High-velocity, large-scale data streams have become pervasive. Frequently, the associated labels for such data prove costly to measure and are not always available upfront. Consequently, the analys...

Gaussian graphical regression is a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which permits the response variables and covariates to outnumbe...

We present parametric and semiparametric latent Markov time-interaction processes, that are point processes where the occurrence of an event can increase or reduce the probability of future events....

In this work, we develop a new ensemble learning framework, multi-label Random Subspace Ensemble (mRaSE), for multi-label classification. Given a base classifier (e.g., multinomial logistic regress...

With ever increasing number of features of modern datasets, data heterogeneity is gradually becoming the norm rather than the exception. Whereas classical regressions usually assume all the samples...

Qini curves have emerged as an attractive and popular approach for evaluating the benefit of data-driven targeting rules for treatment allocation. We propose a generalization of the Qini curve to m...

Manifold learning obtains a low-dimensional representation of an underlying Riemannian manifold supporting high-dimensional data. Kernel density estimates of the low-dimensional embedding with a fi...

In this paper, we present two efficient methods for sampling from the Watson distribution in arbitrary dimensions. The first method adapts the rejection sampling algorithm from Kent et al. (2018), ...

The configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network’s s...

For a given n, what is the smallest number k such that every sequence of length n is determined by the multiset of all its k-subsequences? This is called the k-deck problem for sequence reconstruction, and has been generalized to the two-dimensional case – reconstruction of n×n-matrices from submatrices. Previous works show that the smallest k is at most O(n12) for sequences and at most O(n23) for

Strong orthogonal arrays have better space-filling properties than ordinary orthogonal arrays for computer experiments. Strong orthogonal arrays of strengths two plus, two star and three minus can improve the space-filling properties in low dimensions and column orthogonality plays a vital role in computer experiments. In this paper, we use difference matrices and generator matrices of linear codes

The Additive Voronoi Tessellations (AddiVortes) model is a multivariate regression model that uses Voronoi tessellations to partition the covariate space in an additive ensemble model. Unlike other...

Nonparametric regression suffers from curse of dimensionality, requiring a relatively large sample size for accurate estimation beyond the univariate case. In this paper, we consider a simple metho...

Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantee...

Sumner's universal tournament conjecture states that every (2n−2)-vertex tournament should contain a copy of every n-vertex oriented tree. If we know the number of leaves of an oriented tree, or its maximum degree, can we guarantee a copy of the tree with fewer vertices in the tournament? Due to work initiated by Häggkvist and Thomason (for number of leaves) and Kühn, Mycroft and Osthus (for maximum