fig1 illustrates an exemplary multihop ring type local area network ( lan ) in accordance with the present invention in which six network interface units ( nius ) 101a - 101f are interconnected by means of a four channel communications medium , the channels of which may be separated from each other , for example , in space , time , or frequency . in accordance with one embodiment of the invention , each niu is arranged to transmit directly to at least a first other niu in the network and to receive directly from at least a second other niu in the network . for example , niu 101a is arranged to transmit directly to only niu 101f , and to receive directly from only niu 101e , both by means of channel 102b . in accordance with another embodiment of the invention , several of the nius are arranged not to transmit directly to other nius in the network . rather , these nius communicate with each other by multihopping packets of data through various intermediate nius . for example , a packet to be transmitted from niu 101a to niu 101b would first be transmitted via channel 102b from niu 101a to niu 101fthen retransmitted by niu 101f to niu 101d via channel 102a , and finally retransmitted by niu 101d by means of channel 102c to destination niu 101b . an alternative path that would effect the same communication would be from niu 101a to niu 101f via channel 102b , from niu 101f to niu 101e via channel 102b , from niu 101e to niu 101c via channel 102d , and finally from niu 101c to destination niu 101b via channel 102d . every niu in the network of fig1 is capable of communicating with every other niu in the network either directly or by means of one or more intermediate nius in the manner described above . although the packet must go through several intermediate nius , many of the other nius connected in the network are bypassed , shortening packet delay time and saving processing power at each niu . the connectivity pattern , which specifies the nius each particular niu will be arranged to transmit directly to , can be chosen such that the number of required channels and the number of required intermediate nius by which a packet must be processed is kept small . in another embodiment of the invention , a shufflenet connectivity pattern of the prior art , an exemplary one of which is shown in fig2 is implemented using the inventive lan of fig1 . the shufflenet connectivity pattern is desirable because the number of nius in the network is kp k , where p and k are any positive integers , and data from an niu in the network can reach any other niu in at most 2k - 1 hops . the general rule defining a complte shufflenet connectivity pattern is as follows : first , a set of kp k nius , each with p receivers and p transmitters , is arranged into k columns , numbered 0 through k - 1 , of p k nius each . for example , fig2 shows a set of ( 3 ) ( 2 3 )= 24 nius arranged into 3 columns of 2 3 nius each . the rightmost column of fig2 shown in dashed outline , is repetitive of first column 224 and is shown only for the purpose of constructing the logic diagram . any connections to nius in the rightmost column of fig2 would actually be made to the corresponding niu in first column 224 of fig2 when the network is implemented . the first niu in column i of the shufflenet , where 0 ≦ i ≦ k - 1 , has each of its p transmitters connected to a separate one of the receivers of the first p nius in column i + 1 ( mod k ). thereafter , each consecutive niu in column i is arranged to transmit directly to the next p nius in column i + 1 ( mod k ), until the p . sup . ( k - 1 ) th niu in column i is reached . since each niu in column i is arranged to transmit directly to p nius in column i + 1 ( mod k ), the p . sup . ( k - 1 ) th niu in column i will communicate with the last p nius in column i + 1 ( mod k ). the transmitters of each consecutive group of p . sup . ( k - 1 ) nius in column i are then configured identically to the first group . in column 224 of fig2 for example , nius 200 , 203 , 206 and 209 , all located in first column 224 , each transmit directly to a separate pair of nius in second column 225 . nius 212 , 215 , 218 and 221 , the remainder of the nius from column 224 , transmit to the same pairs of nius as nius 200 , 203 , 206 and 209 , respectively . the mod k addition is utilized in the above description in order to establish the connections from the last column of nius to the first column of nius . one technique for implementing the shufflenet connectivity pattern on a multiple channel ring type network is to run the multiple channel medium up and down alternate columns of the shufflenet pattern , and connect each of the nius to the appropriate channels . this implementation is shown in fig3 . although this technique produces a ring type network with a small number of required intermediate hops , the number of channels required on the medium is at least p . sup . ( k + 1 ). this number of required channels can be reduced by installing the nius along the multiple channel medium in a special sequence such that each of the channels can be reused . to determine the special sequence in which to dispose the nius , define a cycle of the shufflenet as a set of k nius , one from each of the k columns of the shufflenet , such that a transmitting niu can receive its own transmitted data in exactly k hops by multihopping it through the set of k nius . for example , nius 206 , 213 , and 205 of fig2 form a cycle since a packet transmitted from niu 206 can reach itself by being hopped from niu 206 to niu 213 , from niu 213 to niu 205 and from niu 205 to niu 206 . fig4 shows the 24 niu shufflenet of fig2 the connections between the nius of fig4 being identical to those of fig2 . the nius of fig4 have been arranged so that each cycle makes up a row of nius , and the cycles are numbered 0 through 7 , from top to bottom , using a binary numbering system . fig4 also shows that an niu transmits directly only to other nius which are either located in the same cycle or are located in a cycle which differs in its binary representation by exactly one digit . for example , niu 210 is located in cycle 101 of fig4 and transmits directly to niu 220 , located in the same cycle , and to niu 223 , located in cycle 111 . the binary numerals 111 and 101 differ only in the middle digit . from fig4 it can also be seen that there are no nius in exemplary cycle 101 that transmit directly to any nius in exemplary cycle 011 , since both the first and the second digits of the numerals 101 and 011 are different . this property is used to derive the special sequence in which to dispose the nius for a ring type implementation of the shufflenet pattern by : ( 1 ) disposing the nius of each cycle in a prescribed sequence , adjacent to each other , along the ring , and ( 2 ) disposing the cycles along the ring in sequence such that every cycle is preceded and followed by a cycle which differs in its binary representation by one bit . using this physical implementation , the maximum number of channels required to implement a ( p , k ) shufflenet on a ring type network is : ## equ1 ## the above mentioned prescribed sequence is determined as follows : arrange the nius of a cycle in a sequence such that each niu transmits directly to the next niu in the sequence , except for the last niu in the sequence which transmits directly to the first niu in the sequence . for example , the nius of cycle 010 of fig4 could be arranged 213 , 205 , and 206 , since , as fig4 shows , niu 213 transmits directly to niu 205 , niu 205 transmits directly to niu 206 , and niu 206 transmits directly to niu 213 . the sequence of nius within any cycle must then be cyclically shifted until a sequence is obtained which requires no more channels within the cycle than the number of channels required between cycles as specified by the above equations . arranging each cycle of the shufflenet in a similar manner will result in the nius on the ring being disposed in a special sequence which keeps the required number of channels small . fig5 shows the shufflenet of fig4 implemented on a ring type lan by using multiple channel communications medium 501 sequentially routed from one niu to the next . in accordance with an embodiment of the invention , the nius in any particular cycle are disposed adjacent to each other along communications medium 501 , and the cycles which differ in their binary representations by one digit are also disposed adjacent to each other along communications medium 501 . the network of fig5 exemplifies several important aspects of the invention which allow the required number of channels , as well as the required number of intermediate nius which must process each packet , to be kept small . first , with the exception of one niu in each cycle , each niu is installed adjacent to the one niu from the same cycle to which it is configured to transmit directly . second , for any two cycles which are installed adjacent to each other , at least one niu from one of the cycles is configured to transmit directly to at least one niu from the other of the two cycles . finally , each niu is able to transmit directly to or receive directly from a plurality of other nius which may be located anywhere in the sequence of nius but which follow the shufflenet connectivity pattern of fig2 and 4 . the positions of these other nius , to which an niu is arranged to transmit directly or from which an niu is arranged to receive directly , relative to the niu , are different for many of the nius in the network . for example , niu 210 of fig5 transmits directly to nius 220 and 223 , which are each adjacent on the ring to niu 210 , but receives directly from nius 215 and 203 , which are separated on the ring from niu 210 by one and eight nius , respectively . niu 211 , on the other hand , transmits directly to nius 221 and 218 , separated on the ring from niu 211 by zero and one nius , respectively , and receives directly from nius 216 and 204 , separated on the ring from niu 211 by zero and eight nius , respectively . this nonlinearity of the direct communications links is a result of the logical connection pattern being implemented , and results in a relatively small required number of intermediate hops when compared with prior art ring type networks , which have linear connection patterns . in another aspect of the invention , a criss - cross connectivity pattern is implemented using the multiple channel communications medium and the ring - type architecture described above . fig6 shows an exemplary criss - cross connectivity pattern which can be defined as a plurality of n 2 nius , where n is an even integer , arranged logically into an n × n matrix , 4 × 4 in this example , with the rows and columns of the matrix being each numbered 0 through n - 1 , and the niu in the rth row and cth column being designated niu ( r , c ). furthermore , the nius are configured to transmit directly to surrounding nius according to the following rule : if r is odd and c is odd : niu ( r , c ) transmits directly to niu ( r , c + 1 ), niu ( r , c - 1 ), niu ( r + 1 , c - 1 ), niu ( r + 1 , c + 1 ), and niu ( r + 1 , c ) if r is odd and c is even : niu ( r , c ) transmits directly to niu ( r , c + 1 ), niu ( r , c - 1 ), niu ( r - 1 , c - 1 ), niu ( r - 1 , c + 1 ), and niu ( r - 1 , c ) if r is even and c is odd : niu ( r , c ) transmits directly to niu ( r , c + 1 ), niu ( r , c - 1 ), niu ( r - 1 , c - 1 ), niu ( r - 1 , c + 1 ), and niu ( r + 1 , c ) if r is even and c is even : niu ( r , c ) transmits directly to niu ( r , c + 1 ), niu ( r , c - 1 ), niu ( r + 1 , c - 1 ), niu ( r + 1 , c + 1 ), and niu ( r - 1 , c addition and subtraction in the above niu indices are defined modulo n so that the last row and last column are connected to the first row and first column respectively . further , it is to be understood that the use of odd and even column numbers is for the purpose of explanation only and that the connection patterns of alternating rows and columns relative to each other , regardless of the numbers they are assigned , is the preferred embodiment . this connectivity pattern is considered efficient for multihop networks because the maximum number of hops required for a packet to reach any destination niu from any source niu can be reduced to n / 2 . fig7 shows only the horizontal connections of the exemplary 4 × 4 criss - cross connectivity pattern shown in fig6 . it is to be understood that the bottom row and rightmost column of fig6 is repetitive of the top row and leftmost column , respectively in fig6 and is only shown in fig6 in order to display the logical connectivity pattern . accordingly , any logical connections to the bottom row and rightmost column of fig6 have been replaced in fig7 by physical connections to the top row and leftmost column of fig7 and the bottom row and rightmost column of fig6 have been eliminated in fig7 . each of the nius in fig7 is inserted serially into two channels 701 and 702 and the nius located in the last and first columns of fig7 are also inserted into two additional channels 703 and 704 to establish the wraparound connections . the dashed lines in fig7 represent sections of the four channels 701 , 702 , 703 , and 704 which are not used to interconnect any nius but are shown only to more clearly display the ring type structure of the network . fig8 shows the physical connections needed to implement the vertical logical connections of fig6 . each of the channels used to effect these vertical connections is stretched to conform to the path of the multiple channel communications medium . the diagonal connections of fig6 may be implemented via separate channels , in a manner similar to that of the vertical connections shown in fig8 or they may be multiplexed onto the existing channels . fig9 shows an example , using nius 605 , 606 , 609 , and 610 of fig6 of how to multiplex the diagonal connections onto the existing channels . in this example , understood to be for illustrative purposes only and not as limiting the scope of the invention , each of the channels is a fiber optic filament capable of supporting a lightwave signal and the multiplexing means used by the nius is frequency division multiplexing ( fdm ). each filament in fig9 is numbered to correspond to the channel number from fig7 or 8 which the filament represents . more particularly , niu 605 transmits data onto filament 801 at two frequencies ; f1 for data destined for niu 609 , and f2 for data destined for niu 610 . niu 609 receives both frequencies , interprets data at f1 as being destined for itself , but relays data at f2 to niu 610 by means of filament 701 . this could be accomplished using , for example , a selective wavelength filter , which filters out f1 but couples f2 from filament 801 to filament 701 . thus the diagonal connection between niu 605 and niu 610 is implemented by multiplexing it onto existing filaments 801 and 701 . similarly , niu 609 transmits data onto filament 701 at two frequencies ; f1 for data destined for niu 610 and f3 for data destined for niu 606 . niu 610 receives all three frequencies f1 , f2 , and f3 on filament 701 and interprets data on frequencies f1 and f2 as being destined for itself and as having been transmitted from nius 609 and 605 , respectively . transmissions at frequency f3 are forwarded by niu 610 to niu 606 by means of filament 802 , also using an exemplary selective wavelength filter . niu 606 receives all the data on filament 802 , however frequencies f1 and f3 represent data transmitted from nius 610 and 609 , respectively . filament 702 is used to implement the direct transmission paths from niu 610 to niu 609 , and from niu 605 to niu 606 , and any of the frequencies is acceptable for use on this filament since no multiplexing is required . finally , it should be noted that although the section of filament 701 of fig9 which provides direct communications from niu 606 to niu 605 is shown in fig9 as carrying only frequency f1 , there would actually be three frequencies on this filament because of the diagonal connections between nius 606 and 601 and between nius 602 and 605 , not shown in fig9 . the multiplexing system described above requires that filament 801 carry data on f1 and f2 and that filament 802 carry data on channels f1 and f3 . furthermore , two of the four horizontal filaments 701 , 702 , 703 and 704 will each have to carry data on three different frequencies . in general , to implement the criss - cross connectivity pattern for n 2 nius on a ring type network would require 3n + 4 channels , n for the vertical connections , 4 for the horizontal connections , and 2n for the diagonal connections . using the multiplexing method described above , the network can be implemented with n + 4 channels . the ring implementation of the criss - cross connectivity pattern is similar to that of the shufflenet in that each niu shares common links , one each , with a plurality of other nius and that the positions of the other nius with which a first niu shares a common link , relative to the first niu , are different from the positions of the other nius with which a second niu shares a common link , relative to the position of the second niu .