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This paper proposes a web map system for drawing an arbitrary travel route using a mouse-sensitive following path suggestion. The interaction model of the system allows users to intuitively understand the sequence of user actions needed to draw a conceived route and reduces the number of user actions required. Moreover, the system allows users to understand at a glance several drawing alternatives (static suggestion) and also consider a particular drawing alternative (dynamic suggestion) without making any commitment. The proposed architecture of the system reduces the influence caused by communication delay between a map server and a web client by delivering in advance road network data from a map server to a web client. Experimental evaluations on a prototype we developed demonstrated that the proposed system enables users to draw arbitrary routes within noticeably less clicks, in less time, and with less stress than previous systems