SU748428A1 - Device for resolution of graph into trees - Google Patents

Description

Union of Soviet Socialist Republics

USSR State Committee for Inventions and Discoveries

DESCRIPTION OF THE INVENTION

TO AUTHOR'S CERTIFICATE (61) Additional to author. certificate-wu (22) Declared 10.03.78 (21) 2588679 / 18-24 with the addition of application N9 (23) Priority Published on 07.15.80. Bulletin N9 26

Date of publication of the description 15.0780 (72) Author of the invention

Chervyatsov (71) Applicant

(.,) 748 428 (51) M. CL /

G About G 7/122 (53) UDC 681. zzz (088.8) /

(54) DECOMPOSITION DEVICE

ON TREES

The invention relates to computer technology and can be used in the field to determine the characteristics of decomposition of a graph into trees when studying the reliability of systems displayed by probability graphs.

A device is known for searching for the great-trees of a directed graph, ’θ containing a key matrix, ring switches, a clock generator, triggers, AND circuits, delay circuits, a blocking cell, an inverter. This device allows 15 to reduce the number of clock pulses required to search for all the right. trees in a directed graph by eliminating partial graphs in which the components not related to the root contained in the previously considered partial graphs are repeated. This device is characterized by the following disadvantages: the inability to investigate an undirected * 5 graph) the inability to determine the number of trees formed with the participation of each individual edge of the graph; the inability to control the process of tree formation; 30 the inability to determine the characteristics of the decomposition of the graph into trees.

* A device for finding trees of the graph £ 2] is known, which contains an indication unit, counters, diodes, switches, delay line, blocks of conversion factors, counters of the number of trees. The following disadvantages are inherent in this device: the inability to determine the number of trees formed with the participation of each individual edge of the graph · the inability to control the process of tree formation; the inability to determine the characteristics of the decomposition of the graph into trees.

The closest technical solution to the invention is a device for determining the number of trees [3], containing the And element, the inputs of which are connected to the outputs of the first typesetting field, the inputs of which are connected to the outputs of the keys, the output of the And element is connected to the counting input of one counter and to the first inputs of the elements And the first group, the outputs of which are connected to the counting inputs of other * counters, the reset outputs of the counters and the zero inputs of the triggers (N -1) of the groups are connected to the reset input of the device, the single inputs of the triggers (m -1) of the groups of enes with the recording device inputs. In addition, the device contains a state enumeration unit.

The disadvantages of the prototype are: the lack of control over the process of tree formation; the inability to determine the characteristics of the decomposition of the graph into trees. The characteristics of the decomposition of a graph into trees are the numbers of subsets in which the trees have one, two, etc. edges constant.

The purpose of the invention is to increase the accuracy of research by implementing the additional function of determining the numbers of subsets in which trees have one, two, etc., edges, and represent the possibility of controlling the process of tree formation.

The goal is achieved by the fact that in the device / containing the AND element, the inputs of which are connected to the outputs of the first typesetting field, the inputs of which are connected to the key outputs, the output of the And element is connected to the counting input of one counter and to the first inputs of the And elements of the first group, the outputs of which are connected to the counter inputs of other counters, the outputs of the counter reset and the zero inputs of the triggers, (b \ - 1) groups are connected to the reset input of the device, the individual inputs of the triggers (M - 1) of the groups are connected to the recording inputs of the device, delay elements are introduced, sec I group of AND elements, forbidden elements, the second and third typesetting fields and (N -1) distributors, the inputs of the first distributor are connected to the unit outputs of the triggers of the first group, the inputs of the remaining distributors are connected to the outputs of the inhibit elements, the first inputs of which are connected to the unit outputs of triggers other groups. · the second inputs of the ban elements are connected to the outputs of the second dialed field, the outputs (N - 1) of the distributors are connected to the inputs of the third dialed field, the outputs of which are connected to the control inputs of the keys, directs input (. The N -1) th distributor is connected to the input of the device’s clock pulses and to one of the inputs of the elements of the second group, the other inputs of which are connected to the control outputs of the respective valves, the output of the first element of the second group is connected to the output of the device, the outputs of the remaining elements of the second group are connected to the control inputs of the respective valves and through the delay elements to the second inputs of the corresponding elements of the first group, the read input of the first typesetting field is connected to the polling input of the device wa, the inputs of the second typesetting field are connected to the outputs of the first N -2 distributors.

Functional diagram of the device shown in the drawing.

The device contains an element And 1, the first type-setting field 2, keys (ribs), counters 4 ₂ t 4 _K , elements And 5 _{H And the} first group, triggers

6 _{4 <} m (ribs), prohibition elements 7 _14- r 7 _n _4, _m _ _a , valves m θΝΌ second set-up field 9, elements I 104-10 ₍ ^ of the second group, third set-up field 11, delay elements 12 ₂ = 12 _Ν .,, Reset input 13, clock input 14, polling input 15, stop pulse output 16, recording input 17. In triggers 6 ·,, is the vertex number, j is the number of the edge incident to this vertex.

In the operation of the device, two stages should be distinguished: the stage of setting the graph structure and the stage of studying the graph structure.

Consider the step of setting the graph structure. The basis for specifying a graph in the device is a graph having N vertices of the nth M edges, in which all elements are renumbered. Elements of the device are ordered in accordance with the accepted numbering. Vertex numbers are assigned to the distributors 8 and the inputs., Of the And element 1. The number of distributors is -1, the number of inputs of the And 1 element is H. The numbers of edges incident to the vertices are assigned to the input and output circuits of the distributors 8. The numbers increase from left to right.

On a typesetting field 2, the inputs of the Element I 1 and the keys (edges) 3 ^ m 3 _{m are} connected into a topological diagram of the graph. On the type-setting field 11, the outputs of the distributors 8 and the inputs of the keys 3 corresponding to the edges of the same name in the graph are interconnected. On the type-setting field 9, the outputs of the distributors 8 and the inputs of the inhibit elements 7, corresponding to the edges of the same name, but incident to different vertices, are interconnected. In this case, the rule is observed: the output of the distributor corresponding to the vertex with the lower number must be connected to the input of the same prohibition element corresponding to the vertex with the higher number.

In the future, at the stage of studying the graph, the operation of the device proceeds in steps. In the first cycle, a signal is received at the reset input 13 to the zero inputs of the triggers 6 and the erasing inputs of the counters 4. The triggers and counters are set to their initial state.

In the second cycle, in accordance with the incidence matrix, signals are sent to the unit inputs of triggers 5 (edges) 6, which are set to state 1. From the unit outputs of triggers b (edges) incident to the first vertex, signals are sent to the inputs of the distributor of the first vertex. From the single outputs of the triggers b (edges) incident to the other vertices, the signals are fed to the inputs of the corresponding distributors via the inhibit elements 7. In each 15 distributor, one output corresponding to the excited input with a lower number is excited. The signals from the outputs of the distributors come through the switching circuit of the dial field 9 to the inputs of the corresponding inhibit elements 7, and through the switching circuit of the dial field 11 to the inputs of the corresponding keys 3. In this case, the signals at the same __ outputs of the distributors corresponding to ^ ³ corresponding vertices with senior numbers are prohibited . As a result, only one output will be excited in each distributor, and among the excited outputs there will not be the same output. The excited outputs will have lower numbers from the set of allowed numbers.

Upon receipt of signals at the control inputs of the keys 3 · 35 electrical contact is formed between their poles.

In the third cycle, a signal is received at the input of the polling 15, which is supplied to through the switching circuit of the type-setting field 2 4Q. inputs of the element And 1. If the excited outputs of the distributors correspond to the edges forming a tree, then the element And 1 is activated and from its output a signal is sent to the post-45 ice counter 4.

In the fourth cycle, a signal is input to the input of clock pulses 14, which is fed to the control input of the last distributor 8 and inputs of elements I 10. At the same time, the next one is excited by the number of allowed outputs of the last distributor 8. Further operation of the device proceeds by alternating the third '__ and fourth cycles as long as ³³ is not energized the last of the last authorized distributor outlets. Then — from the control output of the distributor, a signal is sent to the enable input of the corresponding element And 10. The next signal fed to the input of clock pulses 14 passes to the input of the 14'4th, and through the element 10 to the input (4-2- of the distributors and the input of the N-2nd element. 65 delay 12. If the conditions for tree formation are met, then when the signal arrives at the input of the polling 15, element I 1 will work. As a result, a signal is received at the inputs of the N-th and N -1 counters. In this case, the alternate allowed output in the N -2nd dispenser is excited and excites I am the youngest of the allowed outputs of the N -1th distributor (taking into account the new state of the N-2nd distributor) .. Thus, each distributor is transferred to a new state when a signal is received at input 14, if the distributors with the highest numbers are in the last from allowed states.

The operation of the device is terminated if all valves are installed in the last of the allowed states. Then, when the next signal arrives at input 14, all the And 10 elements are triggered. The signals from the outputs of the And 10 elements return the valves to their original state, and the signal from the output of the first And 10 element is a stop signal for the device. The reading of the Nth counter 4 corresponds to the number of trees in the graph. The reading of the N -1th counter 4 corresponds to the number of subsets in which the trees have N-2 constant edges. The readings of the N -2nd counter correspond to the number of subsets in which the trees have N -3 constant edges, etc. · '

Thus, thanks to the introduction of new elements and links between them, the accuracy and depth of the study of the decomposition of the graph into trees increased.

Devices.o allows you to determine the characteristics of the decomposition of the graph into trees. The readings of the counters are characteristic for the accepted numbering of the vertices in the graph. Therefore, it is possible to control the process of tree formation, since with a change in this numbering the sequence of tree formation changes. In addition, the proposed device allows you to work with graphs in which the number of vertices and edges can be variable.

Claims (1)

The invention relates to the field of computer technology and can be used to determine the characteristics of the decomposition of a graph into trees in the study of the reliability of systems displayed by probability graphs. . . It is known a device l for searching the target-tree of the directional graph, containing a key matrix, ring switches, a clock generator, triggers, AND schemes, a delay circuit blocking a cell, an inverter. This device reduces the number of clock pulses needed to search for all the right. trees in a directed graph by excluding partial graphs in which non-root components contained in previously considered partial graphs are repeated. This device is characterized by the following disadvantages: the lack of opportunity to investigate an undirected graph; the inability to determine the number of trees formed with the participation of each individual edge of the graph; the inability to control the process of tree formation; the inability to determine the characteristics of the decomposition of a graph into trees. A device is known for locating the trees of graph 2, containing an indication unit, counters, diodes, switches, a delay line, blocks of conversion factors, counters of the number of trees. The following drawbacks are inherent in this device: the inability to determine the number of trees formed with the participation of each individual edge of the graph, the inability to control the process of tree formation} the inability to determine the characteristics of decomposition of a tree graph. The closest technical solution to the invention is a device for determining the number of L3 trees containing an AND element, the inputs of which are connected to the outputs of the first typed field, whose inputs are connected to the outputs of keys, the output of the AND element connected to the counting input of one counter and to the first inputs of AND elements the first group, the outputs of which are connected to the counting inputs of other counters, the reset outputs of the counters and the zero inputs of the trigger (N -1) groups are connected to the input from the Sa Devices, single inputs of three headers (N -1) groups are connected s with input recording device. In addition, the device contains a brute force block. The disadvantages of the prototype are the inability to control the process of tree formation; the inability to determine the characteristics of the decomposition of the graph into trees. Characteristics of the decomposition of a graph into trees are the numbers of subsets in which the trees have one, two, etc., constant edges. The purpose of the invention is to improve the accuracy of the study by implementing an additional function of determining the numbers of subsets in which trees have one, two, etc., and constant edges, and to provide the ability to control the process of tree formation. The goal is achieved by the fact that a device containing an AND element, whose inputs are connected to inputs of the first typed field, whose inputs are combined with the outputs of keys, AND's stroke is connected to the counting input of one counter and to the first inputs of the AND elements of the first group whose outputs are connected with the counter inputs of other counters, the reset outputs of the counters and the zero inputs of the triggers. (n - 1) groups are connected to the device reset input, the single inputs of the trigger (M - 1) groups are connected to the recording inputs of the device, delay elements are entered, sec and the group of elements And, the elements of the prohibition, the second and third razor-type fields and (N -1) distributors, the inputs of the first distributor are connected to the unit outputs of the tractors of the first group, the inputs of the remaining valves are connected to the outputs of the inhibit elements, the first inputs of which are connected to the unit the trigger outputs of the remaining groups .- the second inputs of the elements of the bar are connected to the outputs of the second dialed floor, the outputs (N - 1) of the distributors are connected to the inputs of the third dialed floor, the outputs of which are connected to the control keys That the terminal (a control. The i-th distributor is connected to the input of the clock pulses of the device and with one input of the elements of the second group, the other inputs of which are connected to the control outputs of the corresponding distributors, the output of the first element of the second group is connected to the output of the device, the outputs of the other elements of the second group are connected to the control inputs of the respective distributors and through the delay elements to the second inputs of the corresponding elements AND of the first group, the read input of the first typed field is connected to the input of the device polling a, v. moves of the second type-setting field are connected to the outputs of the first N -2 distributors. Functional diagram of the device shown in the drawing. The device contains an element And 1, the first type-setting field 2, keys, (edges), counters 4 ,, elements And 5, 5 of the first group, triggers b t CN ,,. (ribs), prohibition elements / t / r, 4-, N- / 8 t BM dispensers, second dial pad 9, And 10 4 elements — Yut — second group, third pad 11, delay elements 12 4- ,, reset input 13, clock input 14, polling input 15, stop pulse output 16, recording input 17, At triggers 6, is the number of the vertex, j is the edge number incident to this vertex. The device should be divided into two stages: the task of setting the structure of the graph and the stage of studying the structure of the graph. Consider the stage of setting the graph structure. The basis for setting a graph in a device is a graph having N vertices and M edges, in which all elements are renumbered. Elements of the device are arranged in accordance with the accepted numbering. Vertex numbers are assigned to distributors 8 and inputs-, element 1. And the number of valves is equal to H -1, the number of inputs to element 1 is equal to H. Edge numbers, incident to the vertices are assigned to the input and output chains of valves 8. The numbers increase from left to right. In the typing field 2, the inputs of the element And 1 and the keys (edges) 3, g 3 are connected to a topological graph scheme. In the set field 11, the outputs of the distributors 8 and the inputs of the keys 3 corresponding to the same edges of the graph are interconnected. On the dial field 9, the outputs of the distributors 8 and the inputs of the prohibition elements7 corresponding to the same edges, but incident to different vertices, are connected each other. In this case, the rule is observed: the output of the distributor corresponding to the vertex with a smaller number must be connected to the I / O device of the same-named element of the denied corresponding to the vertex with a higher number. Later on, at the stage of graph investigation, the operation of the device proceeds in cycles. In the first cycle, a signal is received at the reset input 13 to the zero inputs of the flip-flops 6 and the erasing inputs of the counters 4. The flip-flops and the counters are reset. In the second cycle, in accordance with the incidence matrix, signals are received for single inputs of triggers (edges) 6, which are set to state 1, From single outputs of triggers b (edges) incident to the first vertex, signals are received to the inputs of the distributor of the first vertex C of single outputs triggers b (edges) incident to the other vertices, the signals arrive at the inputs of the corresponding distributors through prohibition elements 7. In each distributor, one output is excited, corresponding to the excited input with a smaller number. Signals from the outputs of the distributors go through the switching circuit of the dial-in lane 9 to the inputs of the corresponding prohibition elements 7, and through the switching circuit of the dial-in field 11 to the inputs of the corresponding switches 3. At the same time, the signals at the same-named outputs of the distributors corresponding to the vertices with higher numbers are prohibited. As a result, only one output will be excited in each distributor, and among the excited outputs there will not be the same output. The excited outputs will have smaller numbers from the set of allowed numbers. When signals arrive at the control inputs of the keys, 3 forms an electrical contact between their field themselves. In the third cycle, a signal arrives at the input of the poll 15, which through the switching circuit of the dial-up field 2 arrives at. the inputs of the element AND 1. If the excited outputs of the distributors correspond to the edges forming the tree, the element 1 triggers and from its output a signal is sent to the latest counter 4. In the fourth cycle, a signal arrives at the input of the clock pulses 14, which is fed to the control the input along the late distributor 8 and the inputs of the And 10 elements. In this case, the next by number of the allowed ones in the turns of the last distributor 8 is excited. Further operation of the device proceeds by alternating the third and fourth cycles until en the last of the last authorized distributor outlets. Then, from the control output of the distributor, a signal is applied to the enabling input of the corresponding element AND 10. The next signal arriving at the input of the clock pulses 14 passes to the input M; th, and through the element AND 10. on the internal clock (C-7 of the distributors and the input M 2 of the delay element 12. If the tree formation conditions are fulfilled, then when a signal arrives at the input of the interrogator: a 15, the element AND 1. As a result, a signal is received at the inputs of the Nth and N -1th counters, thus triggering the sequential allowed output at the N-2d distributor and the youngest of the allowed ones is excited (taking into account the new state of the N-2nd distributor a) outputs of the S1 –1 distributor. Thus, the transfer of each distributor to a new state is carried out with the post If the valves with the highest numbers are in the last of the allowed states, the device is terminated if all the valves are set to the last of the allowed states. Then, when the next signal arrives at the input 14, all And 10 elements are triggered. The signals from the outputs of the elements And 10 bring the valves to the initial state, and the signal from the output of the first element And 10 is a signal to stop the operation of the device. The reading of the N-th counter 4 corresponds to the number of trees in the graph. The indication of -1 counter 4 corresponds to the number of subsets in which the trees have N-2 constant edges. The -2 meter readings correspond to the number of subsets in which trees have H -3 constant edges, etc. Thus, due to the introduction of new elements and the connections between them, the accuracy and depth of the study of the decomposition of the graph into trees has increased. The device allows to determine the characteristics of the decomposition of the graph into trees. The meter readings are characteristic of the received numbering of the vertices in the graph. Consequently, it is possible to control the process of tree formation, since the sequence of tree formation changes with the change of this numbering. In addition, the proposed device allows working with graphs in which the number of vertices and edges can be variable. The invention The device for decomposing a graph into a tree containing an element And whose inputs are connected to the outputs of the first typed field, the inputs of which are connected to the outputs of keys, the output of the element And connected to the counting input of one counter and the first inputs of the elements of the first group whose outputs are connected with counting inputs of other counters, outputs feriTT-n, --- L. r ° - .. are connected to the recording inputs of the device, characterized by the TRM that, in order to increase the accuracy, elements of SINTERNING Z1PET / ° are entered into it, elements of nonnl (and the third in distributors, the inputs of the first distributor are connected to the single outputs of the first group trigger, the inputs of the rest of the JSsSoLr dinenth ° ° D are connected to single outputs of the trigger en ° P ° Db1 to the “tp P” paths connected to the outputs of the second dialed floor, the outputs from the P inputs of P dalitel are connected to the inputs of the third dialed floor, the outputs of which are connected to the controls The control inputs of the keys, the control input N -1} of the distributor are connected to the input of clock pulses, ySSpoftics and with the same inputs of the elements AND the second group, the other inputs of which are connected to the control outputs of the corresponding valves, the output of the first element and the second group is connected to the output of the device, the outputs of the remaining elements and the second group are connected to the control inputs of the corresponding distributors and through the delay elements to the second inputs of the corresponding elements and the first group, the read input of the first set the floor is connected to the input of the device interrogation .The inputs of the second to yGy ° / ° connected to outputs of the first N -2 valves. Sources of information taken into account in the examination number certificate of the USSR № 271906, cl. G 06 G 7/48, 1969 № USSR certificate № 364939, cl. G 06 G 7/48 1971 OQ ,. USSR certificate 329538, cl. G About G 7/48, 1970 prototype). / 7 17 17 G7 17 7 17 P  I i. one-.. one}