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This work aims at minimize the cost of answering snapshot multi-predicate queries in high-communication-cost networks. High-communication-cost (HCC) networks is a family of networks where communicating data is very demanding in resources, for example in wireless sensor networks transmitting data drains the battery life of sensors involved. The important class of multi-predicate queries in horizontally or vertically distributed databases is addressed. We show that minimizing the communication cost for multi-predicate queries is NP-hard and we propose a dynamic programming algorithm to compute the optimal solution for small problem instances. We also propose a low complexity, approximate, heuristic algorithm for solving larger problem instances efficiently and running it on nodes with low computational power (e.g. sensors). Finally, we present a variant of the Fermat point problem where distances between points are minimal paths in a weighted graph, and propose a solution. An extensive experimental evaluation compares the proposed algorithms to the best known technique used to evaluate queries in wireless sensor networks and shows improvement of 10% up to 95%. The low complexity heuristic algorithm is also shown to be scalable and robust to different query characteristics and network size.