Generating paired sequences with maximal compatibility from a given set is one of the most important challenges in various applications, including information and communication technologies. However, the number of possible pairings explodes in a double factorial order as a function of the number of entities, manifesting the difficulties of finding the optimal pairing that maximizes the overall reward. In the meantime, in real-world systems, such as user pairing in non-orthogonal multiple access (NOMA), pairing often needs to be conducted at high speed in dynamically changing environments; hence, efficient recognition of the environment and finding high reward pairings are highly demanded. In this paper, we demonstrate an efficient pairing algorithm to recognize compatibilities among elements as well as to find a pairing that yields a high total compatibility. The proposed pairing strategy consists of two phases. The first is the observation phase, where compatibility information among elements is obtained by only observing the sum of rewards. We show an efficient strategy that allows obtaining all compatibility information with minimal observations. The minimum number of observations under these conditions is also discussed, along with its mathematical proof. The second is the combination phase, by which a pairing with a large total reward is determined heuristically. We transform the pairing problem into a traveling salesman problem (TSP) in a three-layer graph structure, which we call Pairing-TSP. We demonstrate heuristic algorithms in solving the Pairing-TSP efficiently. This research is expected to be utilized in real-world applications such as NOMA, social networks, among others.
翻译:在现实世界系统中,如用户在非横向多重访问中配对(NOMA),配对往往需要在动态变化的环境中高速进行;因此,在各种应用中,包括信息和通信技术中,需要高度的对环境的高效认识和找到高报酬配对。然而,在本文中,我们展示了一种有效的配对算法,以确认各元素之间的兼容性,并找到能够产生高度完全兼容性的配对法。提议的配对战略分为两个阶段。第一个是观察阶段,各元素之间的兼容性信息只能通过观察奖励总和(NOMA),我们展示了一种高效的战略,在动态变化的环境中可以获取所有兼容性信息;因此,对环境的高效认识和找到高报酬配对网络的要求很高。在本文中,我们展示了一种有效的配对算法,在这个阶段中,我们将一个混合阶段的PMA 与一个高层次的数学结构联系起来。我们将一个预估的预估的预估的预估的预估的PMA 。我们将一个预估的预估的预估的预估的预估的预估的预估的预估的预估的预估的预估的预估的预估的预估的预估的预估的预算, 将一个预估的预估的预估的预估的预估的预估的预估的预估的预估的预估的预估的预估的预算的预估的预估的PMA的预算的预的预的预的折的折式的折式的 将是一个一比程。