Filter array to retain rows with smallest element count and unique first and last elements

use current and end

$all = array();
foreach ($var as $idx=>$arr):
  $first = current($arr);
  $last  = end($arr);
  $size  = count($arr);
  $key   = $first.'.'.$last;
  if (isset($all[$key])):
    if ($size > $all[$key]):
      unset($var[$idx]);
    else:
      $all[$key] = $size;
    endif;
  else:
    $all[$key] = $size;
  endif;
endforeach;

ops ... you can iterate (again) at the end to ensure the already reduced sized array can be further removed

In general, yes, you are too worried about efficiency (as you wondered in another comment). Though PHP is not the most blisteringly-fast language, I would suggest building the most straightforward solution, and only worry about optimizing it or streamlining it if there is a noticeable issue with the end result.

Here is what I would do, off the top of my head. It is based off of ajreal's answer but hopefully will be easier to follow, and catch some edge cases which that answer missed:

// Assume $var is the array specified in your question

function removeRedundantRoutes( $var ){

    // This line sorts $var by the length of each route
    usort( $var, function( $x, $y ){ return count( $x ) - count( $y ); } );

    // Create an empty array to store the result in
    $results = array();

    // Check each member of $var
    foreach( $var as $route ){
        $first = $route[0];
        $last = $route[ count( $route ) - 1 ];
        if( !array_key_exists( "$first-$last", $results ) ){
            // If we have not seen a route with this pair of endpoints already,
            // it must be the shortest such route, so place it in the results array
            $results[ "$first-$last" ] = $route;
        }
    }

    // Strictly speaking this call to array_values is unnecessary, but
    // it would eliminate the unusual indexes from the result array
    return array_values( $results );
}