Version 5.0 The LEDA User Manual

void SWEEP SEGMENTS(const list& S, GRAPH & G,
bool embed = false, bool use optimization = true)
as above.
The algorithm ([11]) runs in time O((n + s) log n) + m), where n is the
number of segments, s is the number of vertices of the graph G, and m
is the number of edges of G. If S contains no overlapping segments then
m = O(n+s). If embed is true the running time increases by O(m log m).
If use optimization is true an optimization described in the LEDA book
is used.
void MULMULEY SEGMENTS(const list& S,
GRAPH & G, bool embed = false)
as above.
There is one additional output convention. If G is an undirected graph,
the undirected planar map corresponding to G(s) is computed. The computation
follows the incremental algorithm of Mulmuley ([68]) whose expected
running time is O(M + s + n log n), where n is the number of
segments, s is the number of vertices of the graph G, and m is the number
of edges.
void SEGMENT INTERSECTION(const list& S,
void (∗report)(const segment& , const segment& ))
takes a list of segments S as input and executes for every pair (s 1 , s 2 ) of
intersecting segments report(s 1 , s 2 ). The algorithm ([6]) has running time
O(nlog 2 n + k), where n is the number of segments and k is the number
intersecting pairs of segments.
void SEGMENT INTERSECTION(const list& S, list& P )
takes a list of segments S as input, computes the set of (proper) intersection
points between all segments in S and stores this set in P . The
algorithm ([11]) has running time O((|P | + |S|) log |S|).
• Red-Blue Line Segment Intersection
void SEGMENT INTERSECTION(const list& S1 , const list& S2 ,
GRAPH & G, bool embed = false)
takes two lists of segments S 1 and S 2 as input and computes the planar
graph G induced by the set of straight line segments in S 1 ∪S 2 (as defined
above). Precondition: Any pair of segments in S 1 or S 2 , respectively, does
not intersect in a point different from one of the endpoints of the segments,
i.e. segments of S 1 or S 2 are either pairwise disjoint or have a common
endpoint.
• Closest Pairs