Wordpress - Optimizing a Proximity-based Store Location Search on a Shared Web Host?

This might be too late for you, but I'm going to reply anyway, with a similar answer as I gave to this related question, so future visitors can refer to both questions.

I would not store these values in the post metadata table, or at least not only there. You want a table with post_id, lat, lon columns, so you can place an index of lat, lon and query on that. This should not be too hard to keep up to date with a hook on post save and update.

When you query the database, you define a bounding box around the starting point, so you can do an efficient query for all lat, lon pairs between the North-South and East-West borders of the box.

After you get this reduced result, you can do a more advanced (circular or actual driving directions) distance calculation to filter out the locations that are in the corners of the bounding box and therefor further away than you desire.

Here you find a simple code example that works in the admin area. You need to create the extra database table yourself. The code is ordered from most to least interesting.

<?php
/*
Plugin Name: Monkeyman geo test
Plugin URI: http://www.monkeyman.be
Description: Geolocation test
Version: 1.0
Author: Jan Fabry
*/

class Monkeyman_Geo
{
    public function __construct()
    {
        add_action('init', array(&$this, 'registerPostType'));
        add_action('save_post', array(&$this, 'saveLatLon'), 10, 2);

        add_action('admin_menu', array(&$this, 'addAdminPages'));
    }

    /**
     * On post save, save the metadata in our special table
     * (post_id INT, lat DECIMAL(10,5), lon DECIMAL (10,5))
     * Index on lat, lon
     */
    public function saveLatLon($post_id, $post)
    {
        if ($post->post_type != 'monkeyman_geo') {
            return;
        }
        $lat = floatval(get_post_meta($post_id, 'lat', true));
        $lon = floatval(get_post_meta($post_id, 'lon', true));

        global $wpdb;
        $result = $wpdb->replace(
            $wpdb->prefix . 'monkeyman_geo',
            array(
                'post_id' => $post_id,
                'lat' => $lat,
                'lon' => $lon,
            ),
            array('%s', '%F', '%F')
        );
    }

    public function addAdminPages()
    {
        add_management_page( 'Quick location generator', 'Quick generator', 'edit_posts', __FILE__  . 'generator', array($this, 'doGeneratorPage'));
        add_management_page( 'Location test', 'Location test', 'edit_posts', __FILE__ . 'test', array($this, 'doTestPage'));

    }

    /**
     * Simple test page with a location and a distance
     */
    public function doTestPage()
    {
        if (!array_key_exists('search', $_REQUEST)) {
            $default_lat = ini_get('date.default_latitude');
            $default_lon = ini_get('date.default_longitude');

            echo <<<EOF
<form action="" method="post">
    <p>Center latitude: <input size="10" name="center_lat" value="{$default_lat}"/>
        <br/>Center longitude: <input size="10" name="center_lon" value="{$default_lon}"/>
        <br/>Max distance (km): <input size="5" name="max_distance" value="100"/></p>
    <p><input type="submit" name="search" value="Search!"/></p>
</form>
EOF;
            return;
        }
        $center_lon = floatval($_REQUEST['center_lon']);
        $center_lat = floatval($_REQUEST['center_lat']);
        $max_distance = floatval($_REQUEST['max_distance']);

        var_dump(self::getPostsUntilDistanceKm($center_lon, $center_lat, $max_distance));
    }

    /**
     * Get all posts that are closer than the given distance to the given location
     */
    public static function getPostsUntilDistanceKm($center_lon, $center_lat, $max_distance)
    {
        list($north_lat, $east_lon, $south_lat, $west_lon) = self::getBoundingBox($center_lat, $center_lon, $max_distance);

        $geo_posts = self::getPostsInBoundingBox($north_lat, $east_lon, $south_lat, $west_lon);

        $close_posts = array();
        foreach ($geo_posts as $geo_post) {
            $post_lat = floatval($geo_post->lat);
            $post_lon = floatval($geo_post->lon);
            $post_distance = self::calculateDistanceKm($center_lat, $center_lon, $post_lat, $post_lon);
            if ($post_distance < $max_distance) {
                $close_posts[$geo_post->post_id] = $post_distance;
            }
        }
        return $close_posts;
    }

    /**
     * Select all posts ids in a given bounding box
     */
    public static function getPostsInBoundingBox($north_lat, $east_lon, $south_lat, $west_lon)
    {
        global $wpdb;
        $sql = $wpdb->prepare('SELECT post_id, lat, lon FROM ' . $wpdb->prefix . 'monkeyman_geo WHERE lat < %F AND lat > %F AND lon < %F AND lon > %F', array($north_lat, $south_lat, $west_lon, $east_lon));
        return $wpdb->get_results($sql, OBJECT_K);
    }

    /* Geographical calculations: distance and bounding box */

    /**
     * Calculate the distance between two coordinates
     * http://stackoverflow.com/questions/365826/calculate-distance-between-2-gps-coordinates/1416950#1416950
     */
    public static function calculateDistanceKm($a_lat, $a_lon, $b_lat, $b_lon)
    {
        $d_lon = deg2rad($b_lon - $a_lon);
        $d_lat = deg2rad($b_lat - $a_lat);
        $a = pow(sin($d_lat/2.0), 2) + cos(deg2rad($a_lat)) * cos(deg2rad($b_lat)) * pow(sin($d_lon/2.0), 2);
        $c = 2 * atan2(sqrt($a), sqrt(1-$a));
        $d = 6367 * $c;

        return $d;
    }

    /**
     * Create a box around a given point that extends a certain distance in each direction
     * http://www.colorado.edu/geography/gcraft/warmup/aquifer/html/distance.html
     *
     * @todo: Mind the gap at 180 degrees!
     */
    public static function getBoundingBox($center_lat, $center_lon, $distance_km)
    {
        $one_lat_deg_in_km = 111.321543; // Fixed
        $one_lon_deg_in_km = cos(deg2rad($center_lat)) * 111.321543; // Depends on latitude

        $north_lat = $center_lat + ($distance_km / $one_lat_deg_in_km);
        $south_lat = $center_lat - ($distance_km / $one_lat_deg_in_km);

        $east_lon = $center_lon - ($distance_km / $one_lon_deg_in_km);
        $west_lon = $center_lon + ($distance_km / $one_lon_deg_in_km);

        return array($north_lat, $east_lon, $south_lat, $west_lon);
    }

    /* Below this it's not interesting anymore */

    /**
     * Generate some test data
     */
    public function doGeneratorPage()
    {
        if (!array_key_exists('generate', $_REQUEST)) {
            $default_lat = ini_get('date.default_latitude');
            $default_lon = ini_get('date.default_longitude');

            echo <<<EOF
<form action="" method="post">
    <p>Number of posts: <input size="5" name="post_count" value="10"/></p>
    <p>Center latitude: <input size="10" name="center_lat" value="{$default_lat}"/>
        <br/>Center longitude: <input size="10" name="center_lon" value="{$default_lon}"/>
        <br/>Max distance (km): <input size="5" name="max_distance" value="100"/></p>
    <p><input type="submit" name="generate" value="Generate!"/></p>
</form>
EOF;
            return;
        }
        $post_count = intval($_REQUEST['post_count']);
        $center_lon = floatval($_REQUEST['center_lon']);
        $center_lat = floatval($_REQUEST['center_lat']);
        $max_distance = floatval($_REQUEST['max_distance']);

        list($north_lat, $east_lon, $south_lat, $west_lon) = self::getBoundingBox($center_lat, $center_lon, $max_distance);


        add_action('save_post', array(&$this, 'setPostLatLon'), 5);
        $precision = 100000;
        for ($p = 0; $p < $post_count; $p++) {
            self::$currentRandomLat = mt_rand($south_lat * $precision, $north_lat * $precision) / $precision;
            self::$currentRandomLon = mt_rand($west_lon * $precision, $east_lon * $precision) / $precision;

            $location = sprintf('(%F, %F)', self::$currentRandomLat, self::$currentRandomLon);

            $post_data = array(
                'post_status' => 'publish',
                'post_type' => 'monkeyman_geo',
                'post_content' => 'Point at ' . $location,
                'post_title' => 'Point at ' . $location,
            );

            var_dump(wp_insert_post($post_data));
        }
    }

    public static $currentRandomLat = null;
    public static $currentRandomLon = null;

    /**
     * Because I didn't know how to save meta data with wp_insert_post,
     * I do it here
     */
    public function setPostLatLon($post_id)
    {
        add_post_meta($post_id, 'lat', self::$currentRandomLat);
        add_post_meta($post_id, 'lon', self::$currentRandomLon);
    }

    /**
     * Register a simple post type for us
     */
    public function registerPostType()
    {
        register_post_type(
            'monkeyman_geo',
            array(
                'label' => 'Geo Location',
                'labels' => array(
                    'name' => 'Geo Locations',
                    'singular_name' => 'Geo Location',
                    'add_new' => 'Add new',
                    'add_new_item' => 'Add new location',
                    'edit_item' => 'Edit location',
                    'new_item' => 'New location',
                    'view_item' => 'View location',
                    'search_items' => 'Search locations',
                    'not_found' => 'No locations found',
                    'not_found_in_trash' => 'No locations found in trash',
                    'parent_item_colon' => null,
                ),
                'description' => 'Geographical locations',
                'public' => true,
                'exclude_from_search' => false,
                'publicly_queryable' => true,
                'show_ui' => true,
                'menu_position' => null,
                'menu_icon' => null,
                'capability_type' => 'post',
                'capabilities' => array(),
                'hierarchical' => false,
                'supports' => array(
                    'title',
                    'editor',
                    'custom-fields',
                ),
                'register_meta_box_cb' => null,
                'taxonomies' => array(),
                'permalink_epmask' => EP_PERMALINK,
                'rewrite' => array(
                    'slug' => 'locations',
                ),
                'query_var' => true,
                'can_export' => true,
                'show_in_nav_menus' => true,
            )
        );
    }
}

$monkeyman_Geo_instance = new Monkeyman_Geo();

What precision do you need? if it's a state/national wide search maybe you could do a lat-lon to zip lookup and have precomputed distance from zip area to zip area of the restaurant. If you need accurate distances that won't be a good option.

You should look into a Geohash solution, in the Wikipedia article there is a link to a PHP library to encode decode lat long to geohashs.

Here you have a good article explaining why and how they use it in Google App Engine (Python code but easy to follow.) Because of the need to use geohash in GAE you can find some good python libraries and examples.

As this blog post explains, the advantage of using geohashes is that you can create an index on the MySQL table on that field.