We look at the classic problem of resource allocation in computing and communication. There is a rapid surge in device density across different computing and communication platforms, which makes resource allocation in a centralized fashion impractical. The increased density, coupled with low-latency applications, is leading to infrastructures adopting distributed resource allocation schemes. In our work, we build a mathematical model that can be extended to multiple applications like large-scale data centers and ultra-reliable low-latency communication. The resource allocation problem translates to a bipartite matching problem subject to communication constraints. We propose a degree-biased matching algorithm, which selects a receiver probabilistically based on local information, to improve the mean matching size. We observed numerically that the performance of the algorithm degrades with increasing degree of sender connections, and therefore introduced the concept of thinning. By incorporating thinning along with the greedy receiver selection, the mean matching size is enhanced, along with a reduction in the communication overhead, leading to lower latency. The problem is hard due to its combinatorial complexity. We conducted simulations with different topologies and workloads to validate the efficiency of our proposed algorithm. The results showed that our algorithm outperformed the baseline in the crucial performance metrics. We have submitted our work to TNET and are waiting for reviews. Meanwhile, we are working towards the extension where we take the system dynamics into consideration for the model.