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The most widely used medium access control (MAC) scheme for underwater acoustic communication (UWAC) networks is conventional time-division multiple access (TDMA), in which only a single node transmits at each time. Since this TDMA is the bottleneck in high traffic networks, in this paper we present a new MAC protocol for UWAC ad-hoc networks that applies spatial reuse to improve network throughput. More specifically, in the proposed protocol selected additional nodes can transmit simultaneously to the active TDMA node, thus improving the efficiency of the MAC protocol. By tracking the time-varying network topology, our protocol adaptively optimizes the set of active nodes and overcomes problems of UWAC networks such as the near-far problem, flickering, and formation of islands. We report performance results for both the conventional TDMA protocol and the proposed protocol from a sea trial at the Haifa harbor. The results show that the new protocol greatly increases the availability of nodes to transmit messages, which leads to an improved overall network throughput in high traffic networks.