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Traceback Defensive Player

I. Strategy Description

The Traceback Player is similar to the Chaser strategy. The Traceback Player consists of a game supplied number of Traceback Robots. Each Traceback Robot is, for the most part, independent. One exception is that they check a global boolean array that indicates whether an enemy robot has already been targetted by another Traceback Robot. An addition to this exception could be to poll each Traceback Robot looking for a target for a score for each available enemy robot. This additional level of cooperation should ensure a higher degree of optimal opponent selection.


Before Traceback

Step 1: Trail Computation

Step 2: Locating the Trail's Closest Point

Step 3: Target Acquisition

Step 4: Traversal to the Closest Point

Step 5: Traceback


Legend: Blue[1] - Traceback Robot / Orange[3] - Enemy Robot

Step-by-Step

Each Traceback Robot performs the following steps to traceback trails left behind an opponent robot.

  1. Trail Computation: A trail is computed for each enemy robot. Each trail consists of a number of segments, each of which has a direction. The whole trail is limited to some constant in order to prevent excessive computation.
  2. Locating the Trail's Closest Point: A closest point is computed by each Traceback robot for each enemy robot. Since the closest point is contained in the closest segment, the closest segment is found.
  3. Target Acquisition: Each Traceback Robot uses the following equations to compute its optimal target to oppose. If the target has been selected already, the Traceback Robot continues selecting the enemy robot with next highest score.

    t = Round Number
    f = Traceback Player's Index
    i = Player Index
    j = Robot Index
    N = Total Number of Players
    M = Board Dimension
    alpha = Weight for Points
    beta = Scale (to make RobotScore an integer)

  4. Traversal to the Closest Point: The Traceback Robot will move towards the closest point calculated in Step (2).
  5. Traceback: The Traceback Robot will trace over the trail that its opponent had created. It will discontinue its current traceback if some point along the trail is no longer possesses its opponent's color or if the trail ends.

II. Reasons behind Strategy

Though chasing, a parasitic strategy, seems like an easy method for disrupting the enemy while potentially gaining some territory, it can be defeated by a common counter-strategy which causes the chasee robot to simply stop. Another common counter-strategy is to chase the chaser. These both effectively stop the chaser, but in the first case, two robots have worked themselves out of competition. Moreover, in the second case, two robots must now counter act the effects of one robot chaser. These are not desirable in games that have more than two players. In these games, the player(s) not being chased will have a distinct advantage. Traceback Player attempts to balance the strengths of chasing with its obvious drawbacks and also spread its effect across multiple opposing players.

One element to balancing the strengths and weaknesses of the Chaser is how to choose an opponent. Choosing an opponent is a critical aspect which affects the success of the Traceback Player or even a Chaser Player could be. Other players, which require choosing opponents, like the Chaser, might use distance to judge whether an enemy robot is an ideal target. While distance is certainly a sensible choice, it does not fully encompass all the criteria needed to pick a good target. Besides distance, the Trackback Player uses the player scores as an additional dimension to its selection scheme. A player score may positively or negatively bias an opponent's robots which may or may not be the closest amongst all neighboring unfriendly robots. If a Traceback Robot must choose between the closest robot who's player is in last place and a slight farther robot whose player is in first place, the Traceback Robot should probably pick the second of its two choices. Finally, a constant is used to weight the effect of the player score versus the effect of the distance between the Traceback Robot and an enemy robot. The additional of score hopefully improves optimal opponent selection in a game with more than two players.

Once a target has been selected, the second major difference between the Chaser and Traceback strategies becomes apparent. Assuming both strategies direct their robots to move to some point along the enemy robots' trail, the two strategies will meet at a common point and diverge. Detecting a chaser is difficult, but assuming the enemy can detect a chaser, the enemy robot can counteract the chaser. Detecting a Traceback Robot seems significantly harder than noticing a chaser.

Both the Chaser and Traceback strategies result in reactive players. On the other hand, their behavior differs in how long they react to the same opposing robot that they choose to antagonize. Also, the Traceback Robot chooses to disrupt the past work rather than react to the future actions of some enemy robot. The Traceback Robot has a clearly defined limit to how much disruption it will cause before it decides to choose a new opponent. It will stop if its stored trail for its target ends and if the trail changes color from its target's color. Last year's Group3Player00 used a timer that, when it expired, forced a robot strategy reevaluation whether to change strategies or switch chase targets. If the enemy employs a stop on being chased counter-strategy, the enemy could simply wait the timer out and continue the rectangle it was trying to build before it was interrupted by the chaser. Other chaser implementations did not involve a switching or reevaluation strategy, and thus, blindly followed the enemy.

Last year's implementations essentially created independent chasers which didn't collaborate on When each Traceback Robot chooses an opponent, each will cooperate with one another to the point that they will not choose the same opponents. This spreads out the effort by each Traceback Robot. Ultimately, this should result a Player who is more capable handling multiple players at one time.

III. Future Work

Besides the obvious, more technical issue of working out bugs, the Traceback Robot has room for improvement. First, opponent selection could be made even more cooperative than how it's done in the current implementation. Secondly, the opponent selection component could be transplanted into a Chaser player. Obviously, a novel method to complement the opponent selection for terminating the chase needs to be determined and integrated into the Chaser player.

The robots in the current implementation reference a two-dimensional boolean array to check whether an opponent has already been targetted or not. Instead, the Player could query each of its robot for a score for a particular opponent. Whichever robot has the highest score would be assigned the enemy robot in question as its target. Since each Traceback robot can be at a different step in the Traceback process, the Traceback Player could preempt a Traceback Robot if another Traceback Robot can more effectively chase an enemy robot's trail.

Since many Chaser implementations just look for the closest enemy robot to chase, a change in opponent selection could significantly enhance the Chaser strategy. Moreover, if an algorithm to optimally end a chaser's chase could be derived, this might alleviate the problems that chasers have in a multiplayer game. Chasers cannot cover every enemy robot, but a Traceback Robot will concentrate on infringing upon the work of the player who's position most threatens the Traceback Player.

IV. Conclusion

The goal of the Traceback Player is to slow down the enemy's territory acquisition. It inadvertently scores when its robots meander their way to their assigned targets, but ultimately, it's not a serious offensive threat. Group 3's Integrated Player should be much more effective when teamed with a more aggressive player like Localized Man on a Mission and a sensible strategy switching algorithm.

These improvements coupled with the current implementation of Traceback Player and its Chaser cousins could seriously dent many of the aggressive players in their conquest of board space.