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Efficient information dissemination over Mobile Ad hoc Networks (MANET) for urban Disaster/Recovery (D/R) missions is emerging as a very challenging and important research problem. In this paper1, we present an adaptive mobility-assisted data dissemination framework as a solution for Disaster/Recovery missions. Our novel framework is based on "Importance Score" of D/R messages to: (1) optimize the number of disseminations due to the bandwidth limitations in MANET, and (2) discard invalid D/R messages due to memory space limitation on mobile devices. The corresponding "Importance Score" function, a linear combination of priority and deadline, ranks D/R messages according to metrics that obtain maximal area coverage and minimal delay in D/R dissemination. Once the D/R messages are ranked, our adaptive mobility-assisted data dissemination protocol broadcasts the top-k, tuning broadcast period according to network conditions. To ensure performance efficiency, we estimate times-to-send (TTS) to limit unnecessary transmissions. Our experimental results show that the presented framework with corresponding algorithms and protocols efficiently utilizes network bandwidth and node memory space (i.e. memory space at a mobile node), while achieving information coverage and delay objectives.