The paper "Routing with Guaranteed Delivery in ad hoc Wireless Networks" by Prosenjit Bose addresses routing problems in ad hoc wireless networks, which are modeled as unit graphs where nodes are points in the plane and communication is possible if the distance between nodes is less than a fixed unit. The authors present the first distributed algorithms for routing that do not require packet duplication or memory at the nodes while guaranteeing packet delivery to the destination. These algorithms can be extended to broadcasting and geocasting without packet duplication. A key byproduct of the results is a simple distributed protocol for extracting a planar subgraph of a unit graph. The paper also includes simulation results on the performance of the algorithms. The introduction explains the context of mobile ad hoc networks (MANETs) and the challenges of routing in such networks, where hosts have limited knowledge of the network topology. The authors define unit graphs and describe the routing problem, including geocasting and broadcasting. They classify previous algorithms into greedy and flooding categories, highlighting the limitations of each. The paper then details a distributed algorithm, GABRIEL, for extracting a connected planar subgraph from a unit graph. This algorithm uses the Gabriel graph, which is useful for identifying and eliminating edges that are not part of the desired subgraph. The algorithm is shown to compute a connected planar subgraph with a computational cost of \(O(d \log d)\), where \(d\) is the degree of a vertex. The authors describe routing algorithms for planar graphs, including FACE-1 and FACE-2, which are modifications of Kranakis et al.'s algorithm. These algorithms are designed to route packets from a source to a destination, broadcasting, and geocasting. The paper also presents the BROADCAST and GEOCAST algorithms for broadcasting and geocasting, respectively. Experimental results are provided to compare the performance of the proposed algorithms with the geographic distance routing (GEDIR) algorithm. The results show that while the proposed algorithms have lower average dilation, they may have lower delivery rates in sparse graphs. However, combining GEDIR with FACE-2 or GFG can improve both delivery rates and average dilation. The paper concludes by discussing the limitations of the BROADCAST and GEOCAST algorithms and open problems, such as designing algorithms that do not require memory at nodes and take subquadratic time to visit all vertices. The work has implications for the design of routing protocols in mobile networks and suggests directions for further research, including dynamic networks, three-dimensional space, and power-aware routing.The paper "Routing with Guaranteed Delivery in ad hoc Wireless Networks" by Prosenjit Bose addresses routing problems in ad hoc wireless networks, which are modeled as unit graphs where nodes are points in the plane and communication is possible if the distance between nodes is less than a fixed unit. The authors present the first distributed algorithms for routing that do not require packet duplication or memory at the nodes while guaranteeing packet delivery to the destination. These algorithms can be extended to broadcasting and geocasting without packet duplication. A key byproduct of the results is a simple distributed protocol for extracting a planar subgraph of a unit graph. The paper also includes simulation results on the performance of the algorithms. The introduction explains the context of mobile ad hoc networks (MANETs) and the challenges of routing in such networks, where hosts have limited knowledge of the network topology. The authors define unit graphs and describe the routing problem, including geocasting and broadcasting. They classify previous algorithms into greedy and flooding categories, highlighting the limitations of each. The paper then details a distributed algorithm, GABRIEL, for extracting a connected planar subgraph from a unit graph. This algorithm uses the Gabriel graph, which is useful for identifying and eliminating edges that are not part of the desired subgraph. The algorithm is shown to compute a connected planar subgraph with a computational cost of \(O(d \log d)\), where \(d\) is the degree of a vertex. The authors describe routing algorithms for planar graphs, including FACE-1 and FACE-2, which are modifications of Kranakis et al.'s algorithm. These algorithms are designed to route packets from a source to a destination, broadcasting, and geocasting. The paper also presents the BROADCAST and GEOCAST algorithms for broadcasting and geocasting, respectively. Experimental results are provided to compare the performance of the proposed algorithms with the geographic distance routing (GEDIR) algorithm. The results show that while the proposed algorithms have lower average dilation, they may have lower delivery rates in sparse graphs. However, combining GEDIR with FACE-2 or GFG can improve both delivery rates and average dilation. The paper concludes by discussing the limitations of the BROADCAST and GEOCAST algorithms and open problems, such as designing algorithms that do not require memory at nodes and take subquadratic time to visit all vertices. The work has implications for the design of routing protocols in mobile networks and suggests directions for further research, including dynamic networks, three-dimensional space, and power-aware routing.