Journal of Combinatorial Optimization最新文献

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 each block that is mined, and (ii) the transaction fees of those transactions that are included in the mined block. The base reward is fixed by the respective blockchain’s protocol and is not under the miner’s control. Hence, for a miner who wishes to maximize earnings, the fundamental problem is to form a valid block with maximal total transaction fees and then try to mine it. Moreover, in many protocols, including Bitcoin itself, the base reward halves at predetermined intervals, hence increasing the importance of maximizing transaction fees and mining an optimal block. This problem is further complicated by the fact that transactions can be prerequisites of each other or have conflicts (in case of double-spending). In this work, we consider the problem of forming an optimal block, i.e. a valid block with maximal total transaction fees, given a set of unmined transactions. On the theoretical side, we first formally model our problem as an extension of Knapsack and then show that, unlike classical Knapsack, our problem is strongly NP-hard. We also show a hardness-of-approximation result. As such, there is no hope in solving it efficiently for general instances. However, we observe that its real-world instances are quite sparse, i.e. the transactions have very few dependencies and conflicts. Using this fact, and exploiting three well-known graph sparsity parameters, namely treedepth, treewidth and pathwidth, we present exact linear-time parameterized algorithms that are applicable to the real-world instances and obtain optimal results. On the practical side, we provide an extensive experimental evaluation demonstrating that our approach vastly outperforms the current Bitcoin miners in practice, obtaining a significant per-block average increase of 11.34 percent in transaction fee revenues which amounts to almost one million dollars per month.

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 of both edge and vertex flake circles. We compare our approach with existing algorithms for the circle generation on the hexagonal grid. Our approach offers simpler algorithm and an analytical characterization that the other algorithms do not offer. The benefit of an analytical characterization is that it makes the question of the membership of a point to a primitive trivial.

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 study proposes an online zero-inventory algorithm (ZIA) and proves an upper bound of (K+1-frac{K}{theta _2}) on the competitive ratio of ZIA. In addition, a lower bound on the competitive ratio of problem MTSS-ip for any deterministic online algorithm is established. For the case with a large storage size K, a lower bound of (frac{K}{48log _{theta _2} K}) on the competitive ratio for MTSS-ip is proved.

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 MViT-CnG model leverages vision transformers and contrastive learning to capture intricate facial features, ensuring robust performance despite diverse and dynamic facial features. By utilizing contrastive learning, the model's interpretability is significantly enhanced, which is vital for building trust in automated systems and facilitating human–machine collaboration. Additionally, this approach enriches the model's capacity to discern shared and distinct features within facial expressions, improving its ability to generalize across different age groups. Evaluations using the FER-2013 and CK + datasets highlight the model's broad generalization capabilities, with FER-2013 covering a wide range of emotions across diverse age groups and CK + focusing on posed expressions in controlled environments. The MViT-CnG model adapts effectively to both datasets, showcasing its versatility and reliability across distinct data characteristics. Performance results demonstrated that the MViT-CnG model achieved superior accuracy across all emotion recognition labels on the FER-2013 dataset with a 99.6% accuracy rate, and 99.5% on the CK + dataset, indicating significant improvements in recognizing subtle facial expressions. Comprehensive evaluations revealed that the model's precision, recall, and F1-score are consistently higher than those of existing models, confirming its robustness and reliability in facial emotion recognition tasks.

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 for overlaps. To illustrate our method, we apply it to input-output analysis within the context of the Moroccan economy.

A subset ( Ssubseteq 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. The disjunctive total domination subdivision number of G is the minimum number of edges which must be subdivided (each edge in G can be subdivided exactly once) to increase the disjunctive total domination number. Firstly, we prove that the disjunctive total domination subdivision problem is NP-complete in bipartite graphs. We next establish some bounds on disjunctive total domination subdivision.

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 of the tottering, which leads to many problems. Because of this, various problems arise, like a decrease in approximation accuracy and an increase in execution time. In this paper, we propose an accurate and efficient graph edit distance heuristic algorithm that prevents tottering when generating (walk). When generating (walk), the traversed node‘s information is saved into the queue and then proceeds to traverse the next node. Then, it is possible to prevent the tottering by comparing an existing traversed node with an enqueued one. Through this, we propose a new (walk) generation algorithm that prevents generating unnecessary (walk) and applies it to existing algorithms to prevent the tottering.

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 contexts characterized by diverse options. We present two simple greedy algorithms for two budget constraints (total size and individual size) and provide the theoretical analysis for upper bound of the regret value. For the total size budget, the proposed algorithm achieves a (frac{1}{2})-regret upper bound by (tilde{mathcal {O}}left( T^frac{2}{3}(kn)^{frac{1}{3}}Bright) ) where T is the time horizon, n is the number of base arms and B denotes the budget. For the individual size budget, the proposed algorithm achieves a (frac{1}{3})-regret with the same upper bound. Moreover, we conduct numerical experiments on these two algorithms to empirically demonstrate the effectiveness.

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 (PoA) of this game is at least 1.6424 for any (alpha in (0,1)). In particular, the PoA of this game is at least (5/3 approx 1.6667) for any (alpha in (frac{2}{5},1)). Furthermore, we obtain a new upper bound of (h(alpha ) le 31/18 approx 1.7222) on the PoA.

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 the makespan), an online algorithm with the best possible competitive ratio (frac{sqrt{5}+1}{2}approx 1.618) has been established in the literature. We show that, after a slightly modification, this known online algorithm also has the best possible competitive ratio (frac{sqrt{5}+1}{2}approx 1.618) for our problem. Finally, we introduce limited restarts into the above special case and present an online algorithm with a better competitive ratio (frac{11}{7}approx 1.571).