Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!mnetor!uunet!seismo!gatech!hubcap!"Douglas From: "Douglas@hubcap.UUCP Newsgroups: comp.hypercube Subject: Re: Hypercube routing (channel usage) Message-ID: <310@hubcap.UUCP> Date: Thu, 16-Jul-87 09:16:32 EDT Article-I.D.: hubcap.310 Posted: Thu Jul 16 09:16:32 1987 Date-Received: Sat, 18-Jul-87 06:42:34 EDT Sender: fpst@hubcap.UUCP Lines: 65 Approved: hypercube@hubcap.clemson.edu pase%oregon-grad.csnet@RELAY.CS.NET (Douglas M. Pase (me)) writes: 000 -> 001 000 -> 010 000 -> 001 -> 011 ... etc -The channel between nodes 0 and 1 is used in four different cases, between 0 -and 2 in two cases, and 0 and 4 in only one case. [...] elroy!wen-king%cit-vlsi.Caltech.Edu@seismo.css.gov (Wen-King Su) writes: - 000 -(0)-> 001 - 000 -(1)-> 010 - 000 -(0)-> 001 -(1)-> 011 - 000 -(2)-> 100 - 000 -(0)-> 001 -(2)-> 101 - 000 -(1)-> 010 -(2)-> 110 - 000 -(0)-> 001 -(1)-> 011 -(2)-> 111 - -On the countrary, I counted that channels 0, 1, and 2 are each used -exactly 4 times, though they are not all channels coming out of node -0. [...] I see your point, but I think it doesn't help. 110-------------10---------------111 /| /| / | / | 1 | 2 | / | / | / 7 / 6 010---------------9--------------011 | 000 -(8)-> 001 | | | | 000 -(4)-> 010 | | | | 000 -(8)-> 001 -(5)-> 011 | | | | 000 -(0)-> 100 4 | 5 | 000 -(8)-> 001 -(3)-> 101 | 100-------------11----------|----101 000 -(4)-> 010 -(9)-> 110 | / | / 000 -(8)-> 001 -(5)-> 011 -(2)-> 111 | / | / | 0 | 3 | / | / |/ |/ 000---------------8--------------001 The intent of the previous article was to find a solution to the following problem: Assume every node communicates with every other node with equal probability. Minimum response time will be achieved if all channels (0-11) are used equally. Excess contention will occur if one channel receives heavier usage than the others. This, of course, assumes sufficient message traffic. What then would be a static routing algorithm which would uniformly distribute the messages over the channels? Again, assuming uniform message traffic, the previously posted algorithm will place the most messages on channels 8, 9, 10 and 11. The message traffic will be twice that of channels 4, 5, 6, and 7, and four times that of channels 0, 1, 2, and 3. Clearly, a dynamic approach which moves the message nearer to its destination and sellects the channel based on traffic at that time will be the big winner. However, I am looking for a static algorithm which will uniformly distribute messages over the channels. The random algorithms are an interesting possibility I had not thought of, but I'm hoping for a deterministic (not random) approach. (I can get it through enumeration, but that approach is very expensive.) -- Doug Pase -- ...ucbvax!tektronix!ogcvax!pase or pase@Oregon-Grad.csnet