var men_array                     = [
  'm1', 'm2', 'm3', 'm4', 'm5', 'm6', 'm7', 'm8', 'm9', 'm10'
];

var women_array                   = [
  'w1', 'w2', 'w3', 'w4', 'w5'
];

var available_tables_this_round   = [];
var unmet_women                   = [];

// Run round
function start_round(){
	console.log('START OF ROUND ----------------');

    // Set available tables this round
    // One table per woman
    available_tables_this_round = women_array;
  
    // Selected table
    var selected_table;
  
    // Finding table partner for each man
    men_array.forEach(function(item){
        var current_man = item;
        
        // Checking if this user has unmet women on record
        if(typeof unmet_women[current_man] == 'undefined'){
            // Unmet women array not set. Setting...
            unmet_women[current_man] = women_array;
        }
      
        // Loop through available tables to see which
        // of those the man can join (has not visited yet).
        for(var i = 0; i < available_tables_this_round.length; i++){
						var current_woman = available_tables_this_round[i];
            
            // If woman among the available has not been met
            if($.inArray(current_woman, available_tables_this_round) !== -1){
              	selected_table = current_woman;
                
                 // Removing table from those available this round
                 available_tables_this_round = $.grep(available_tables_this_round, function(value) {
                  return value != selected_table;  
                });
              
                // Removing woman from unmet by this man
                unmet_women[current_man] = $.grep(unmet_women[current_man], function(value) {
                  return value != selected_table;   
                });
                
                console.log(current_man, '>>>', selected_table);
              
              	// Exiting loop since we've found a match for the man (for this round!)
                break;
            }
        }        
    });
    
    console.log('END OF ROUND ----------------');
  
    
}

// Button handling
$(document).on('click', 'button#start_round_btn', start_round);

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<button id="start_round_btn">Start Round</button>

function getRounds(men, women) {
    // Exclude the cases where a solution is not possible
    if (men.length > women.length * 2) throw "not possible: too many men"; 
    if (women.length > men.length * 2) throw "not possible: too many women"; 
    // Create the tables:
    // Women get a fixed place, so the table name is the woman's name
    var tables = women.slice();
    // Create the seaters: they are the men
    var seaters = men.slice();
    // Which do we have fewer of? tables or seaters?
    var maxLen = Math.max(tables.length, seaters.length);
    var least = tables.length < maxLen ? tables : seaters;
    // The smallest of both arrays should get some dummies added to it.
    // We insert the dummies at odd indices: This is the main point of this algorithm
    for (var i = 0; least.length < maxLen; i++) least.splice(i*2+1, 0, 'pause');

    // Now everything is ready to produce the rounds. There are just as many
    // rounds as there are tables (including the "pause tables"):
    return tables.map( (_, round) =>    
        // Assign the men: each round shifted one place to the left (cycling):
        tables.map( (table, tid) => [seaters[(round+tid)%maxLen], table] )
    );
}

var result1 = getRounds(["John", "Tim", "Bob", "Alan", "Fred"], 
                        ["Lucy", "Sarah", "Helen"]);
console.log(result1);

var result2 = getRounds(["John", "Tim"],
                        ["Lucy", "Sarah", "Helen", "Joy"]);
console.log(result2);