\chapter*{List of Notations}
\addcontentsline{toc}{chapter}{List of Notations}
\markright{Mudabir Kabir Asathulla \hfill List of Notations \hfill}
$\mathbf{G}$ - bipartite planar graph whose matching is to be computed\par 
$\mathbf{G_{M}}$ - residual graph of $G$ \par
$\mathbf{M}$ - current matching in $G$ \par
$\mathbf{M^*}$ - maximum matching in $G$ \par
$\mathbf{R_j}$ - a region in $r$-division of $G$/$G_M$ \par
$\mathbf{V_j}$ - set of vertices in region $R_j$ \par
$\mathbf{E_j}$ - set of edges in region $R_j$ \par
$\mathbf{\K_j}$ - set of boundary vertices in region $R_j$ \par
$\mathbf{D_j}$ - dense distance graph constructed from $R_j$ \par
$\mathbf{(X,Y)}$ - a bipartite group in Monge decomposition \par
$\mathbf{H}$ - compressed residual graph constructed from $G_M$\par
$\mathbf{B_F}$ - set of free vertices of type $B$ in $G_M$ \par
$\mathbf{A_F}$ - set of free vertices of type $A$ in $G_M$ \par
$\mathbf{V}$ - vertex set of $G$ \par
$\mathbf{V_H}$ - vertex set of $H$ \par
$\mathbf{\RH{j}}$ - a region in $H$ constructed from $R_j$\par
$\mathbf{\Ej}$ - set of edges in $\RH{j}$ \par
$\mathbf{b_j}$ - free internal vertex of type $B$ in $\RH{j}$ \par
$\mathbf{a_j}$ - free internal vertex of type $A$ in $\RH{j}$ \par
$\mathbf{B_H}$ - set of vertices of type $B$ in $H$ \par
$\mathbf{A_H}$ - set of vertices of type $A$ in $H$ \par
$\mathbf{\HSet{B}{F}}$ - set of free vertices of type $B$ in $H$ \par
$\mathbf{\HSet{B}{F}}$ - set of free vertices of type $A$ in $H$ \par
$\mathbf{\N{u}{j}}$ - set of vertices which have an incoming edge from $u$ in  $\RH{j}$ (neighbors of u)\par
$\mathbf{(u,v)}$ - a directed edge from vertex $u$ to vertex $v$ in $G_M$ or $H$ as specified in the context\par
$\mathbf{P}$ - a directed path in $G_M$ \par
$\mathbf{P'}$ - a directed path in $H$ whose projection in $G_M$ is $P$ \par
$\mathbf{L(u)}$ - layer number assigned to vertex $u$ by BFS in the current iteration \par
$\mathbf{S(u)}$ - length of the shortest path to a vertex $u$ from any free vertex in $\HSet{B}{F}$\par
$\mathbf{S'(u)}$ - length of the shortest path from a vertex $u$ to any free vertex in $\HSet{A}{F}$\par
$\mathbf{\Delta}$ - total length of all augmenting paths found in $H$ by FINDAUGPATH\par
$\mathbf{RST_i}$ - 2-D Range search tree constructed from bipartite group $(X_i,Y_i)$ for efficient DFS\par
$\mathbf{RST^*_i}$ - 1-D Range search tree constructed from bipartite group $(X_i,Y_i)$ for efficient BFS without using FR-Dijkstra\par