We con­sider a vari­ant of col­li­sion-free rout­ing prob­lem CRP. In this prob­lem, we are given set $C$ of $n$ ve­hi­cles which are mov­ing in a plane along a pre­de­fined di­rected rec­ti­lin­ear path. Our ob­jec­tive (CRP) is to find the max­i­mum num­ber of ve­hi­cles that can move with­out col­li­sion. CRP is shown to be NP-Hard. It was also shown that the ap­prox­i­ma­tion of this prob­lem is as hard as Max­i­mum In­de­pen­dent Set prob­lem (MIS) even if the paths be­tween a pair of ve­hi­cles in­ter­sects at most once. So we study the con­strained ver­sion CCRP of CRP in which each ve­hi­cle is al­lowed to move in a di­rected L-Shaped Path. We prove CCRP is NP-Hard by a re­duc­tion from MIS in L-graphs, which was proved to be NP-Hard even for unit L-graph. Si­mul­ta­ne­ously, we show that any CCRP can be par­ti­tioned into col­lec­tion L of L-graphs such that CCR Pre­duces to a prob­lem of find­ing MIS in L-graph for each par­ti­tion in L. Thus we show that any al­go­rithm, that­can pro­duce a $\beta$-ap­prox­i­ma­tion for L-graph, would pro­duce a $\beta$-ap­prox­i­ma­tion for CCRP. We show that unit L-graphs in­ter­sected by an axis-par­al­lel line is Co-com­pa­ra­ble. For this prob­lem, we pro­pose an al­go­rithm for find­ing MIS that runs in $O(n^2)$ time and uses $O(n)$ space. As a corol­lary, we get a 2-ap­prox­i­ma­tion al­go­rithm for find­ing MIS of unit L-graph that runs in $O(n^2)$ time and uses $O(n)$ space.