This paper investigates the superposition problem of two or more individual semi-Markov decision processes (SMDPs). The new sequential decision process superposed by individual SMDPs is no longer an SMDP and cannot be handled by routine iterative algorithms, but we can expand its state spaces to obtain a hybrid-state SMDP. Using this hybrid-state SMDP as an auxiliary and inspired by the Robbins–Monro

Sustainable scheduling is getting more and more attention with economic globalization and sustainable manufacturing. However, fewer studies on the batch scheduling problem consider energy consumption. This paper conducts an investigation into the multi-objective hybrid flow shop batch-scheduling problem with the objectives of minimizing both the makespan and electrical energy consumption. The study

The Euclidean Steiner problem is the problem of finding a set \(\mathcal{S}\mathcal{t}\), with the shortest length, such that \(\mathcal{S}\mathcal{t}\cup \mathcal {A}\) is connected, where \(\mathcal {A}\) is a given set in a Euclidean space. The solutions \(\mathcal{S}\mathcal{t}\) to the Steiner problem will be called Steiner sets while the set \(\mathcal {A}\) will be called input. Since every

This paper studies the inefficiency of multiplicative approximate Nash Equilibrium for scheduling games. There is a set of machines and a set of jobs. Each job could choose one machine and be processed by the chosen one. A schedule is a \(\theta \)-NE if no player has the incentive to deviate so that it decreases its cost by a factor larger than \(1+\theta \). The \(\theta \)-NE is a generation of

In this paper, we investigate the data mule scheduling with handling time and time span constraints (DMSTC) in which the goal is to minimize the number of data mules dispatched from a depot that are used to serve target sensors located on a wireless sensor network. Each target sensor is associated with a handling time and each dispatched data mule must return to the original depot before time span

In the production scheduling of prefabricated components, a scheduling model considering the learning effect of processing time and the deterioration effect of delivery time in this paper is provided. More precisely, it asks for an assignment of a series of independent prefabricated jobs that arrived over time to a single machine for processing, and once the execution of a job is finished, it will

Let F(G) and \(F_t(G)\) be the zero forcing number and the total forcing number of a graph G, respectively. In this paper, we study the relationship between the total forcing number of a graph and its vertex covering number (or independence number), and prove that \(F_t(G) \le \Delta \alpha (G)\) and \(F_t(G) \le (\Delta - 1)\beta (G) + 1\) for any connected graph G with the maximum degree \(\Delta

Desktop cloud technology has revolutionized modern computing by enabling remote desktop functionality through cloud computing and virtualization. However, traditional fuzzy set theories struggle with the uncertainties inherent in these environments. This study addresses this gap by introducing the probabilistic p, q-rung orthopair fuzzy model, a novel extension that integrates probabilistic elements

In this paper, we find distributions of the left-to-right maxima, right-to-left maxima, left-to-right minima and right-to-left-minima statistics on up-down and down-up permutations of even and odd lengths. We recover and generalize a result by Carlitz and Scoville, obtained in 1975, stating that the distribution of left-to-right maxima on down-up permutations of even length is given by (sec⁡(t))q.

Recently, Leemans and Stokes constructed an infinite family of incidence geometries admitting trialities but no dualities from the groups PSL(2,q) (where q=p3n with p a prime and n>0 a positive integer). Unfortunately, these geometries are not flag transitive. In this paper, we work with the Suzuki groups Sz(q), where q=22e+1 with e a positive integer and 2e+1 is divisible by 3. For any odd integer

The classification problem of P- and Q-polynomial association schemes has been one of the central problems in algebraic combinatorics. Generalizing the concept of P- and Q-polynomial association schemes to multivariate cases, namely to consider higher rank P- and Q-polynomial association schemes, has been tried by some authors, but it seems that so far there were neither very well-established definitions

Let V be a finite dimensional vector space over a finite field. Suppose that F1, F2, …, Fr are r-cross t-intersecting families of k-subspaces of V. In this paper, we determine the extremal structure when ∏i=1r|Fi| is maximum under the condition that dim⁡(⋂F∈FiF)

Cameron-Liebler sets of generators in polar spaces were introduced a few years ago as natural generalisations of the Cameron-Liebler sets of subspaces in projective spaces. In this article we present the first two constructions of non-trivial Cameron-Liebler sets of generators in polar spaces. Also regular m-ovoids of k-spaces are introduced as a generalization of m-ovoids of polar spaces. They are

We obtain a polynomial criterion for a set to have a small doubling in terms of the common energy of its subsets.

We show that the Terwilliger algebra of a quasi-thin association scheme over a field is always a quasi-hereditary cellular algebra in the sense of Cline-Parshall-Scott and of Graham-Lehrer, respectively, and that the basic algebra of the Terwilliger algebra is the dual extension of a star with all arrows pointing to its center if the field has characteristic 2. Thus many homological and representation-theoretic

We construct simple geometric operations on faces of the Cayley sum of two polytopes. These operations can be thought of as convex geometric counterparts of divided difference operators in Schubert calculus. We show that these operations give a uniform construction of Knutson–Miller mitosis in the type A and Fujita mitosis in the type C on Kogan faces of Gelfand–Zetlin polytopes.

In 1920, Percy Alexander MacMahon defined the partition generating functionsAk(q):=∑0

Cloud computing has a powerful capability to handle a large number of tasks. However, this capability comes with significant energy requirements. It is critical to overcome the challenge of minimizing energy consumption within cloud service platforms without compromising service quality. In this paper, we propose a heuristic energy-saving scheduling algorithm, called Real-time Multi-workflow Energy-efficient

Consider a simple (edge weighted) graph \(G = \left( {V,E} \right)\) with \(\left| V \right| = n\) and \(\left| E \right| = m\). Let \(xy \in E\). The domination of a vertex \(z \in V\) by an edge \(xy\) is defined as \(z\) belonging to the closed neighborhood of either \(x\) or \(y\). An edge set \(W\) is considered as an edge-vertex dominating set of \(G\) if each vertex of \(V\) is dominated by

Determining the minimum genus of a graph is a fundamental optimisation problem in the study of network design and implementation as it gives a measure of non-planarity of graphs. In this paper, we are concerned with determining the smallest value of g such that a given graph G has an embedding on the orientable surface of genus g. In particular, we consider the Cartesian product of graphs since this

In this paper we study a scheduling problem with release dates and submodular rejection penalties on multiple (parallel) identical serial-batch machines. For this problem, each machine processes jobs in batches, jobs in a common batch start and finish simultaneously, and the duration of a batch is equal to the sum of a setup time and the total processing time of jobs in it. Some jobs are accepted and

Consider a set of items, X, with a total of n items, among which a subset, denoted as \(I\subseteq X\), consists of defective items. In the context of group testing, a test is conducted on a subset of items Q, where \(Q \subset X\). The result of this test is positive, yielding 1, if Q includes at least one defective item, that is if \(Q \cap I \ne \emptyset \). It is negative, yielding 0, if no defective

In this paper, a reduced quadratic surface support vector machine (RQSSVM) classification model is proposed and solved using the augmented Lagrange method. The new model can effectively handle nonlinearly separable data without kernel function selection and parameter tuning due to its quadratic surface segmentation facility. Meanwhile, the maximum margin term is replaced by an \(L_2\) regularization

In this paper, intuitionistic fuzzy multi-objective linear fractional programming problems (IFMOLFPs) with several fractional criteria, including profit/cost, profit/time, or profitability ratio maximization, are considered. Moreover, all parameters, with the exception of the decision variables, are characterized as triangular intuitionistic fuzzy numbers. The component-wise optimization method is

The performance of machine learning algorithms is significantly influenced by the quality of the underlying dataset, which often comprises a mix of essential and redundant features. Feature selection, which identifies and discards these redundant features, plays a pivotal role in reducing computational and storage overheads. Current methodologies for this task primarily span filter-based and wrapper-based

Solving the optimal order quantity for products with stock-dependent demand is a challenging task as both exact values of multiple parameters and complicated procedures are required. Motivated by this practical dilemma, this paper develops a new method to overcome the above-mentioned two challenges simultaneously. This new method, referred as two-stage AEOQ (adaptive economic order quantity) policy

An Eulerian orientation is an orientation of the edges of a graph such that every vertex is balanced: its in-degree equals its out-degree. Counting Eulerian orientations corresponds to the crucial partition function in so-called “ice-type models” in statistical physics and is known to be hard for general graphs. For all graphs with good expansion properties and degrees larger than log8⁡n, we derive

Given an r-graph F with r≥2, let ex(n,(t+1)F) denote the maximum number of edges in an n-vertex r-graph with at most t pairwise vertex-disjoint copies of F. Extending several old results and complementing prior work [34] on nondegenerate hypergraphs, we initiate a systematic study on ex(n,(t+1)F) for degenerate hypergraphs F.

Given a grid of active and inactive pixels, the weighted rectangles partitioning (WRP) problem is to find a maximum-weight partition of the active pixels into rectangles. WRP is formulated as an integer programming problem and instances with an integral relaxation polyhedron are characterized by a balanced problem matrix. A complete characterization of these balanced instances is proved. In addition

This paper considers a movement minimization problem for mobile sensors. Given a set of n point targets, the k-Sink Minimum Movement Target Coverage Problem is to schedule mobile sensors, initially located at k base stations, to cover all targets minimizing the total moving distance of the sensors. We present a polynomial-time approximation scheme for finding a \((1+\epsilon )\) approximate solution

Community detection, as a crucial network analysis technique, holds significant application value in uncovering the underlying organizational structure in complex networks. In this paper, we propose a degree and betweenness-based label propagation method for community detection (DBLPA). First, we calculate the importance of each node by combining node degree and betweenness centrality. A node i is

For a connected graph G, an instance I is a set of pairs of vertices and a corresponding routing R is a set of paths specified for all vertex-pairs in I. Let \(\mathfrak {R}_I\) be the collection of all routings with respect to I. The undirected optical index of G with respect to I refers to the minimum integer k to guarantee the existence of a mapping \(\phi :R\rightarrow \{1,2,\ldots ,k\}\), such

For a fixed graph F, a graph G is F-saturated if G does not contain F as a subgraph, but adding any edge in \(E(\overline{G})\) will result in a copy of F. The minimum size of an F-saturated graph of order n is called the saturation number of F, denoted by sat(n, F). In this paper, we are interested in saturation problem of graph \(K_1\vee {P_t}\) for \(t\ge 2\). As some known results, \(sat(n,K_1\vee

We consider a truthful facility location game in which there is a set of agents with private locations on the line of real numbers, and the goal is to place a number of facilities at different locations chosen from the set of those reported by the agents. Given a feasible solution, each agent suffers an individual cost that is either its total distance to all facilities (sum-variant) or its distance

Despite the assortment optimization problem has been widely studied in the past decades, the interplay between advertising and its implications for this issue remains under-explored. This study seeks to bridge this research gap by tackling the combined challenge of advertising and assortment optimization. We assume that advertising can increase the awareness of specific products, and the magnitude

The paper deals with the analysis of the communicative behavior of various types of actors, speech perception and optimization of influence based on social media data and is an extended version of the report presented at CSoNet 2020 and published based on the deliverables of the conference. The paper proposes an improved methodology that is tested on the new material of conflicts regarding urban planning

By considering the parity of the degrees and levels of nodes in increasing trees, a new combinatorial interpretation for the coefficients of the Taylor expansions of the Jacobi elliptic functions is found. As one application of this new interpretation, a conjecture of Ma–Mansour–Wang–Yeh is solved. Unifying the concepts of increasing trees and plane trees, Lin–Ma–Ma–Zhou introduced weakly increasing

This paper concentrates on recursive constructions for 2-designs over finite fields. In 1998, Itoh presented a powerful recursive construction: for certain index λ, if there exists a Singer cycle invariant 2-(l,3,λ)q design, then there also exists an SL(m,ql) invariant 2-(ml,3,λ)q design for all integers m≥3. We investigate the GL(m,ql)-incidence matrix between 2-subspaces and k-subspaces of GF(q)ml

Soprunov and Soprunova posed a question on the existence of infinite families of toric codes that are “good” in a precise sense. We prove that such good families do not exist by proving a more general Szemerédi-type result: for all c∈(0,1] and all positive integers N, subsets of density at least c in {0,1,…,N−1}n contain hypercubes of arbitrarily large dimension as n grows.

Let k≥2 be an integer and let A be a set of nonnegative integers. For a k-tuple of positive integers λ_=(λ1,…,λk) with 1≤λ1<λ2<⋯<λk, we define the additive representation function RA,λ_(n)=|{(a1,…,ak)∈Ak:λ1a1+⋯+λkak=n}|. For k=2, Moser constructed a set A of nonnegative integers such that RA,λ_(n)=1 holds for every nonnegative integer n. In this paper we characterize all the k-tuples λ_ and the sets

A pair (st1,st2) of permutation statistics is said to be r-Euler-Mahonian if (st1,st2) and (rdes, rmaj) are equidistributed over the set Sn of all permutations of {1,2,…,n}, where rdes denotes the r-descent number and rmaj denotes the r-major index introduced by Rawlings. The main objective of this paper is to prove that (excr,denr) and (rdes, rmaj) are equidistributed over Sn, thereby confirming a

Let ex(n,s) denote the maximum number of edges in a triangle-free graph on n vertices which contains no independent sets larger than s. The behaviour of ex(n,s) was first studied by Andrásfai, who conjectured that for s>n/3 this function is determined by appropriately chosen blow-ups of so called Andrásfai graphs. Moreover, he proved ex(n,s)=n2−4ns+5s2 for s/n∈[2/5,1/2] and in earlier work we obtained

The celebrated Kővári-Sós-Turán theorem states that any n-vertex graph containing no copy of the complete bipartite graph Ks,s has at most Os(n2−1/s) edges. In the past two decades, motivated by the applications in discrete geometry and structural graph theory, a number of results demonstrated that this bound can be greatly improved if the graph satisfies certain structural restrictions. We propose

The weak saturation number wsat(n,F) is the minimum number of edges in a graph on n vertices such that all the missing edges can be activated sequentially so that each new edge creates a copy of F. In contrast to previous algebraic approaches, we present a new combinatorial approach to prove lower bounds for weak saturation numbers that allows to establish worst-case tight (up to constant additive

We prove that there exists a function f:N→R such that every directed graph G contains either k directed odd cycles where every vertex of G is contained in at most two of them, or a set of at most f(k) vertices meeting all directed odd cycles. We give a polynomial-time algorithm for fixed k which outputs one of the two outcomes. This extends the half-integral Erdős-Pósa theorem for undirected odd cycles

The motion of a graph is the minimal degree of its full automorphism group. Babai conjectured that the motion of a primitive distance-regular graph on n vertices of diameter greater than two is at least n/C for some universal constant C>0, unless the graph is a Johnson or Hamming graph. We prove that the motion of a distance-regular graph of diameter d≥3 on n vertices is at least Cn/(log⁡n)6 for some

For a linear Hamming metric code of length n over a finite field, the number of distinct weights of its codewords is at most n. The codes achieving the equality in the above bound were called full weight spectrum codes. In this paper, we will focus on the analogous class of codes within the framework of cyclic subspace codes. Cyclic subspace codes have garnered significant attention, particularly for

Let N, P be the sets of all positive integers and odd primes, respectively. In 1991, when studying the existence of abelian difference sets with multiplier −1, S.-L. Ma [14] conjectured that the equation (⁎)x2=22a+2p2n−2a+2pm+n+1, p∈P,x,z,m,n∈N has only one solution (p,x,a,m,n)=(5,49,3,2,1). This is a far from solved problem that has been poorly known for so long. In this paper, using some elementary

In 2017, Aharoni proposed the following generalization of the Caccetta-Häggkvist conjecture: if G is a simple n-vertex edge-colored graph with n color classes of size at least r, then G contains a rainbow cycle of length at most ⌈n/r⌉.

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

For a graph H and an n-vertex graph G, the H-bootstrap process on G is the process which starts with G and, at every time step, adds any missing edges on the vertices of G that complete a copy of H. This process eventually stabilises and we are interested in the extremal question raised by Bollobás of determining the maximum running time (number of time steps before stabilising) of this process over

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

A pair of graphs (Γ,Σ) is called unstable if their direct product Γ×Σ has automorphisms that do not come from Aut(Γ)×Aut(Σ), and such automorphisms are said to be unexpected. In the special case when Σ=K2, the stability of (Γ,K2) is well studied in the literature, where the so-called two-fold automorphisms of the graph Γ have played an important role. As a generalization of two-fold automorphisms,

We study the diametric problem (i.e., optimal anticodes) in the space of permutations under the Ulam distance. That is, let Sn denote the set of permutations on n symbols, and for each σ,τ∈Sn, define their Ulam distance as the number of distinct symbols that must be deleted from each until they are equal. We obtain a near-optimal upper bound on the size of the intersection of two balls in this space

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

We describe a construction of the Tutte polynomial for both matroids and q-matroids based on an appropriate partition of the underlying support lattice into intervals that correspond to prime-free minors, which we call a Tutte partition. We show that such partitions in the matroid case include the class of partitions arising in Crapo's definition of the Tutte polynomial, while not representing a direct

We consider k-graphs on n vertices, that is, F⊂([n]k). A k-graph F is called intersecting if F∩F′≠∅ for all F,F′∈F. In the present paper we prove that for k≥7, n≥2k, any intersecting k-graph F with covering number at least three, satisfies |F|≤(n−1k−1)−(n−kk−1)−(n−k−1k−1)+(n−2kk−1)+(n−k−2k−3)+3, the best possible upper bound which was proved in [4] subject to exponential constraints n>n0(k).