Distributed determination of dynamic frame sizes in a network

1. A communication system, comprising:

devices configured to communicate with each other through a temporal sequence of frames,

wherein each frame includes sub-channels;

wherein a total number of sub-channels in a given frame is dynamically determined based on a transmission schedule;

wherein the transmission schedule is calculated by the devices based on transmission lists that are exchanged between the devices;

wherein a first transmission list for a first device includes a first group of sub-channels reserved by the first device and a second group of sub-channels reserved by a set of devices communicating with the first device; and

wherein the total number of sub-channels is a least common multiple of the number of sub-channels in the transmission lists exchanged between the devices, and wherein the least common multiple is a product of ranks of the transmission lists divided by a largest common divisor of the ranks.

2. The communication system of claim 1 , wherein the first device communicates with a first subset of the set of devices directly.

3. The communication system of claim 2 , wherein the first device communicates with a second subset of the set of devices indirectly, and wherein indirect communication between the first device and a second device is mediated via a third device that communicates directly with the first device.

4. The communication system of claim 3 , wherein the second group of sub-channels includes sub-channels reserved by the first subset of the set of devices and sub-channels reserved by the second subset of the set of devices.

5. The communication system of claim 1 , wherein the first transmission list includes margin for future transmission needs of either or both of the first device and the set of devices.

6. The communication system of claim 5 , wherein the margin includes un-reserved sub-channels for use in communicating between the devices.

7. The communication system of claim 1 , wherein the first transmission list is transmitted by the first device during one or more sub-channels in the first group of sub-channels.

8. The communication system of claim 7 , wherein the first transmission list is exchanged during control portions of the one or more of the sub-channels in the first group of sub-channels.

9. The communication system of claim 1 , wherein the first transmission list includes identifiers for the first device and the set of devices corresponding to the first group of sub-channels and the second group of sub-channels.

10. The communication system of claim 9 , wherein the first device is configured to determine an ordered-transmission list based on the exchanged transmission lists;

wherein the ordered-transmission list include a lexicographical ordering of the identifiers for the sub-channels in the first transmission list; and

wherein the first device is configured to dynamically select sub-channels to reserve based on a ranking of the first device for available sub-channels in the ordered-transmission list.

11. The communication system of claim 10 , wherein the first device is configured to add a sub-channel to the first transmission list if the first device is unable to select a sub-channel to reserve.

12. The communication system of claim 1 , wherein the first transmission list includes updates to either or both of the first group of sub-channels and the second group of sub-channels.

13. The communication system of claim 1 , wherein the transmission schedule allows conflict-free communication between the devices using the sub-channels.

14. The communication system of claim 1 , wherein a time delay between two sub-channels in the first group of sub-channels is less than a pre-determined value.

15. The communication system of claim 1 , wherein a first rank for the first device is a smallest power of a common base number for the communication system which is larger than a number of sub-channels in the first group of sub-channels and the second group of sub-channels.

16. The communication system of claim 1 , wherein the total number of sub-channels is a common multiple of the number of sub-channels in the transmission lists exchanged between the devices.

17. The communication system of claim 1 , wherein the transmission schedule repeats the first transmission list for the first device N times thereby ensuring that transmissions from the first device have the same periodicity as the transmission schedule, and wherein N is an integer.

18. The communication system of claim 1 , wherein the sub-channels correspond to time slots, frequency bands, spread-spectrum codes, or directional antennas that transmit and receive the frames.

19. A communication device, comprising:

a transceiver configured to communicate with other devices through a temporal sequence of frames,

wherein each frame includes sub-channels;

wherein a total number of sub-channels in a given frame is dynamically determined based on a transmission schedule;

wherein the transmission schedule is calculated by the communication device based on a first transmission list collected by the communication device and transmission lists that are exchanged with the other devices;

wherein the first transmission list includes a first group of sub-channels reserved by the communication device and a second group of sub-channels reserved by the other devices; and

wherein the total number of sub-channels is a least common multiple of the number of sub-channels in the transmission lists exchanged between the devices, and wherein the least common multiple is a product of ranks of the transmission lists divided by a largest common divisor of the ranks.

20. A method for communicating between devices, comprising:

transmitting a temporal sequence of frames from a first device, wherein each frame includes sub-channels;

receiving transmission lists from other devices that are communicating with the first device;

collecting a first transmission list for the first device, wherein the first transmission list includes a first group of sub-channels reserved by the first device and a second group of sub-channels reserved by the other devices; and

dynamically calculating a total number of sub-channels in a given frame based on a transmission schedule, wherein the transmission schedule is determined by the first device based on the first transmission list and the received transmission lists; and

wherein the total number of sub-channels is a least common multiple of the number of sub-channels in the transmission lists exchanged between the devices, and wherein the least common multiple is a product of ranks of the transmission lists divided by a largest common divisor of the ranks.