With the advancement of 5G, many communication protocols for data transmission have been developed and put into practice. However, alongside these innovations, the issue of redundancy in packet headers has arisen, leading to concerns such as increased resource utilization, diminished transmission efficiency, and elevated latency in the context of real-time communications like voice-over-IP (VoIP). The existing header compression algorithms, such as robust header compression (RoHC), have fallen short in addressing these contemporary header compression demands, as they are primarily designed for specific headers such as RTP, UDP and IP. Therefore, it's necessary to achieve header optimization in the transfer of packets across various protocol layers and multiple flows, with scalability that can be applied to future 6G communications. This paper introduces optimized header compression (OHC) based on RoHC. OHC efficiently compresses headers over the 5G protocol stack and GPRS tunneling protocol user plane (GTP-U), catering to the requirements of real-time data transmission. Furthermore, OHC also integrates protocol headers from multiple quality-of-service (QoS) flows and multi-layer to perform better. The simulation results show that OHC provides a notable increase in header compression, with a minimum improvement of 45%, resulting in reduced resource demands and lower latency. Additionally, the combination of protocol headers from multiple flows and multiple layers yields further enhanced compression performance.

Although resource management schemes and algorithms for networks are well established, we present two novel ideas, based on graph theory, that solve inverse all shortest path problem. Given a symmetric and non-negative demand matrix, the inverse all shortest path problem (IASPP) asks to find a weighted adjacency matrix of a graph such that all the elements in the corresponding shortest path weight matrix are not larger than those of the demand matrix. In contrast to many inverse shortest path problems that are NP-complete, we propose the Descending Order Recovery (DOR) that exactly solves a variant of IASPP, referred to as optimised IASPP. The network provided by DOR minimized the number of links and the sum of the link weights among all the graphs with the same shortest path weight matrix. Our second proposed algorithm, Omega-based Link Removal (OLR), solves the optimised IASPP by utilising the effective resistance from flow networks. The essence of our idea is the applications of properties of flow networks, such as electrical power grids, to compute the needed resources in path networks subject to end-To-end demands, such as telecommunication networks where quality of service constraints specify the end-To-end demands.