Journal of Combinatorial Optimization最新文献

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 :Rrightarrow {1,2,ldots ,k}), such that (phi (P)ne phi (P')) if P and (P') have common edge(s), over all routings (Rin mathfrak {R}_I). A natural lower bound of the undirected optical index is the edge-forwarding index, which is defined to be the minimum of the maximum edge-load over all possible routings. Let w(G, I) and (pi (G,I)) denote the undirected optical index and edge-forwarding index with respect to I, respectively. In this paper, we derive the inequality (w(T,I_A)<frac{3}{2}pi (T,I_A)) for any tree T, where (I_A:={{x,y}:,x,yin V(T)}) is the all-to-all instance.

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 to the farthest facility (max-variant). For both variants, we show tight bounds on the approximation ratio of strategyproof mechanisms in terms of the social cost, the total individual cost of the agents.

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_1vee {P_t}) for (tge 2). As some known results, (sat(n,K_1vee {P_t})) is determined for (2le tle 4). We will show that (sat(n,K_1vee {P_t})=(n-1)+sat(n-1,P_t)) for (tge 5) and n sufficiently large. Moreover, ((K_1vee {P_t}))-saturated graphs with (sat(n,K_1vee {P_t})) edges are characterized.

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 of this effect is jointly depends on the product-specific effectiveness of advertising and the allocated advertising budget. For this joint problem, our objective is to maximize the expected revenue by finding the optimal advertising strategy and the displayed assortment. In this work, we analyze the structure of this problem and propose efficient approaches to solve it across different scenarios. In the unconstrained setting, we demonstrate that the optimal assortment includes products whose revenue exceeds a certain threshold. When there is a cardinality constraint for the assortment, we consider a relaxed problem and propose an efficient method to identify a near-optimal solution. We also examine the joint assortment, pricing, and advertising problem in both unconstrained and cardinality-constrained settings, incorporating the fairness constraint for the advertising strategy and extending our findings to account for consumer sequential decision-making patterns. Through a series of numerical tests, we confirm the validity of our methods and demonstrate that they outperform existing heuristic approaches.

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 running in time (n^{O(1/epsilon )}) for this problem when k, the number of base stations, is constant. Our algorithm improves the running time exponentially from the previous work that runs in time (n^{O(1/epsilon ^2)}), without any target distribution assumption. To devise a faster algorithm, we prove a stronger bound on the number of sensors in any unit area in the optimal solution and employ a more refined dynamic programming algorithm whose complexity depends only on the width of the problem.

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, computational results on balancedness recognition and on solving WRP are presented.

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 considered as a core node in the network if its importance is maximal among its neighbor nodes. Next, layer-by-layer label propagation starts from core nodes. The first layer of nodes for label propagation consists of the first-order neighbors of all core nodes. In the first layer of label propagation, the labels of core nodes are first propagated to the non-common neighbor nodes between core nodes, and then to the common neighbor nodes between core nodes. At the same time, the flag parameter is set to record the changing times of a node’s label, which is helpful to calibrate the node’s labels during the label propagation. It effectively improves the misclassification in the process of label propagation. We test the DBLPA on four real network datasets and nine synthetic network datasets, and the experimental results show that the DBLPA can effectively improve the accuracy of community detection.

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. The research was conducted on the material of social media concerning the construction of the South-East Chord in Moscow (Russia). The study involved a cross-disciplinary approach using neural network technologies, complex networks analysis. The dataset included social networks, microblogs, forums, blogs, videos, reviews. This paper presents the semantic model for the influence maximization analysis in social networks using neural network technologies, also proposed a variant of analyzing the situation with individual and collective actors, multiple opinion leaders, with a dynamic transformation of the hierarchy and ratings according to various parameters.

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 efficiency of the grid. In this paper, an efficient EV charging technique based on blockchain based user transaction and smart contract is devised. Here, charge scheduling is performed by acquiring the information the charging demand of the EV over Internet of things. In case the EV does not have sufficient power to reach the target, nearest Charging Station (CS) with the minimal electricity price is identified. The CS is selected considering various factors, such average waiting time, distance, power, traffic, and so on. Here, power prediction is performed using the Deep Maxout Network (DMN), whose weights are adapted based on the devised Exponentially Snake Optimization (ESO) algorithm. Furthermore, the efficacy of the devised ESO-DMN is examined considering metrics, like average waiting time, distance, and number of EVs charged and power and is found to have attained values of 1.937 s, 13.952 km, 55 and 2.876 J.

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 a non-tree weight function for (Q_4), we improve the weight function technique, introduced by Hurlbert and extended by Cranston et al., that gives an upper bound for the pebbling number of graphs. Then, we propose a conjecture on weight functions for the n-dimensional cube. We also construct a set of valid weight functions for variations of lollipop graphs, extending previously known constructions.