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I have a data structure, containing time span nodes, with the following properties:

• Nodes are sorted ascending
• Time spans will not overlap, but may have gaps between them
• Each node will have a start datetime and a finish datetime
• The last node's finish may also be null (not finished yet)

I want to be able to find the node that intersects a given datetime, or return false if no match is found — basically resembling the following sql query for a sql table with similar properties as my data structure:

SELECT t.*
FROM table t
WHERE t.start <= probeDate AND
 ( t.finish => probaDate OR
 t.finish IS NULL )

I've concluded that a (variation of a) binary search is probably the most efficient search algorithm. So, this is what I have come up with so far:

<?php
class Node
{
 protected $start;
 protected $finish;
 public function __construct( DateTime $start, DateTime $finish = null )
 {
 $this->start = $start;
 $this->finish = $finish;
 }
 public function getStart()
 {
 return $this->start;
 }
 public function getFinish()
 {
 return $this->finish;
 }
 public function __toString()
 {
 /* for easy displaying of the timespan */
 return $this->start->format( 'H:i:s' ) . ' - ' . ( null !== $this->finish ? $this->finish->format( 'H:i:s' ) : '∞' );
 }
}
class NodeList
{
 protected $nodes;
 public function __construct( array $nodes = array() )
 {
 $this->nodes = $nodes;
 }
 public function find( DateTime $date )
 {
 $min = 0;
 $max = count( $this->nodes ) - 1;
 return $this->binarySearch( $date, $min, $max );
 }
 protected function binarySearch( $date, $min, $max )
 {
 if( $max < $min )
 {
 return false;
 }
 else
 {
 $mid = floor( $min + ( ( $max - $min ) / 2 ) ); 
 $node = $this->nodes[ $mid ];
 $start = $node->getStart();
 $finish = $node->getFinish();
 if( $date < $start )
 {
 return $this->binarySearch( $date, $min, $mid - 1 );
 }
 else if( $date > $finish )
 {
 if( $finish == null )
 {
 return $node;
 }
 else
 {
 return $this->binarySearch( $date, $mid + 1, $max );
 }
 }
 else
 {
 return $node;
 }
 }
 }
}

I am testing it with the following:

$nodes = array(
 new Node( new DateTime( '01:01:00' ), new DateTime( '01:05:00' ) ),
 new Node( new DateTime( '01:06:00' ), new DateTime( '01:10:00' ) ),
 new Node( new DateTime( '01:11:00' ), new DateTime( '01:15:00' ) ),
 new Node( new DateTime( '01:16:00' ), new DateTime( '01:20:00' ) ),
 new Node( new DateTime( '01:21:00' ), new DateTime( '01:25:00' ) ),
 new Node( new DateTime( '01:26:00' ), new DateTime( '01:30:00' ) ),
 new Node( new DateTime( '01:31:00' ), new DateTime( '01:35:00' ) ),
 new Node( new DateTime( '01:36:00' ), new DateTime( '01:40:00' ) ),
 new Node( new DateTime( '01:41:00' ) )
);
$list = new NodeList( $nodes );
$date = new DateTime( '01:00:00' );
for( $i = 0; $i < 100; $i++, $date->modify( '+30 seconds' ) )
{
 $node = $list->find( $date );
 echo 'find: ' . $date->format( 'H:i:s' ) . PHP_EOL;
 echo ( $node !== false ? (string) $node : 'false' ) . PHP_EOL . PHP_EOL;
}

Do you see any inherent flaws and/or ways to improve this algorithm? Perhaps you even know of a more time efficient algorithm to accomplish the same?

PS.: Don't worry about the internal integrity of NodeList and Node (checking for invalid nodes, invalid min and max datetimes, checking overlaps, etc.) — this is just a quick and dirty concept. I'm primarily interested in the search algorithm in NodeList::find() and consequently NodeList::binarySearch().