CN114489232A - Graph network method based on self-feedback iterative coherent Itanium machine - Google Patents

Graph network method based on self-feedback iterative coherent Itanium machine Download PDF

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CN114489232A
CN114489232A CN202210116527.5A CN202210116527A CN114489232A CN 114489232 A CN114489232 A CN 114489232A CN 202210116527 A CN202210116527 A CN 202210116527A CN 114489232 A CN114489232 A CN 114489232A
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罗卫东
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Shanghai Turing Intelligent Computing Quantum Technology Co Ltd
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Abstract

The invention provides a network method based on a self-feedback iterative coherent Italic machine, which is based on an Italic algorithm so as to construct a novel graph network algorithm, namely, a spin matrix of an Italic model is mapped onto a node matrix of the graph network, and finally, the Italic algorithm is used for solving a combined optimization problem. The invention combines the Itanium algorithm and the graph network algorithm, the algorithm adds the characteristics of parallel processing, low power consumption and the like for the graph network algorithm, and the algorithm has higher processing speed compared with the graph network algorithm and can be used for processing specific problems.

Description

Graph network method based on self-feedback iterative coherent Itanium machine
Technical Field
The invention relates to a self-feedback iterative coherence Isci machine and a graph network, in particular to a graph network method based on the self-feedback iterative coherence Isci machine.
Background
The yixin model was originally used to describe solid magnetism and phase transition phenomena in condensed physical, and the meaning and application range of the yixin model are continuously expanded. Scientists have found that a series of problems in condensed physics, neural networks, wireless communication and computational science can be qualitatively and quantitatively described by the model. The combinatorial optimization problem in computational science has a one-to-one correspondence with the Esinc model, and the process of solving the optimal solution of the combinatorial optimization problem is mathematically consistent with the problem of solving the ground state of the Esinc model. The combined optimization problem comprises the categories of number set segmentation, graph segmentation, coloring problems and the like, and the problems have important application values in the scenes of industrial scheduling, medicine design, integrated circuit design, signal processing, finance and the like.
The optical ircin machine can be regarded as a special form of an optical neural network, and is suitable for solving a combined optimization problem of Nondeterministic Polynomial (NP) complexity. The combinatorial optimization problem has NP computational complexity and cannot be solved on a traditional electronic computer, and in order to solve the contradiction, people respectively innovate from two aspects of an acceleration algorithm and a hardware architecture, wherein in the aspect of the hardware architecture, researchers design a series of computing systems which are different from the traditional Von Neumann architecture and are specially used for solving the combinatorial optimization problem, and the schemes comprise optical Itanium machine, quantum annealing, adiabatic quantum computing and the like.
The physical system CIM is a device that can accurately or approximately find the ground state of the Ising Hamiltonian. Among various types of Itanium machines, CIM built by using DOPO network stands out by virtue of the advantages of rapidity of optical evolution, convenience of room-temperature computing environment, high efficiency of output results and the like, and is not like a computing environment which is close to absolute zero degree required by a quantum annealing furnace. Classical annealing utilizes thermal transitions, quantum annealing is based on the quantum tunneling principle, and CIM searches for the global ground state by boosting the gain from bottom to top.
With the rapid development of network and database technologies, graph (graph) data has been widely available in more and more databases. Such as biological information networks (biological networks), social network (social networks) data, knowledge maps (knowledge maps), etc., are very common map data. Especially, with the advent of the big data era today, queries on large-scale graph data have a great number of important applications in real life. Therefore, research on query processing technology of large-scale graph data is urgently needed in real-world applications. Although the existing research work has made great progress on the query processing technology of large-scale graph data, the research for specific queries in many specific environments is still in the preliminary stage, and the application of the existing technology cannot meet the query requirements in the specific environments.
Disclosure of Invention
The present invention is made to solve the above problems, and an object of the present invention is to provide a graph network method based on a self-feedback iterative coherent machine.
The invention provides a graph network method based on a self-feedback iterative coherent Itanium machine, which is used for predicting chemical molecular bond breaking and comprises the following steps: acquiring a node matrix of the chemical molecules; mapping a self-feedback iteration coherent Itanium model spin matrix to a node matrix of a graph network; and obtaining the optimal decomposition product of the chemical molecule by a self-feedback iterative coherent Icin machine.
The graph network method based on the self-feedback iterative coherent Itanium machine provided by the invention also has the following characteristics: each spin in the spin matrix corresponds to a corresponding node of the node matrix, each spin has two spin directions, and each spin corresponds to two different states of each node; the interaction strength between two adjacent spins determines whether two adjacent nodes are connected; if the interaction intensity of two adjacent spins is greater than 0, two corresponding adjacent nodes are mutually connected, and the spins of the two nodes are in the same state; if the interaction strength of two adjacent spins is less than 0, the two nodes corresponding to the two adjacent spins are not connected to each other, and the spins of the two nodes are in opposite states.
The graph network method based on the self-feedback iterative coherent Itanium machine provided by the invention also has the following characteristics: wherein, the self-feedback iterative coherent Icin machine comprises: the compressed laser generating unit is used for injecting compressed vacuum into the laser to form a laser beam with compressed vacuum injection; the modulator unit is used for dividing a compressed state light field into two parts and coupling the two parts with the modulator unit, and discrete time feedback operation is realized by sampling photovoltage; the signal feedback unit is used for detecting an output signal modulated by a feedback signal through the modulator by a photodiode after passing through a PSA annular optical fiber cavity, obtaining a digital signal through an analog-to-digital converter, performing corresponding calculation by a matrix multiplier, realizing discrete time feedback operation by sampling optical voltage, and performing phase modulation by a phase modulator after passing through the digital-to-analog converter so that the output feedback signal is the square of the in-phase component of a coupling optical field.
The graph network method based on the self-feedback iterative coherent Itanium machine provided by the invention also has the following characteristics: wherein the modulator unit is a Mach-Zehnder modulator.
The graph network method based on the self-feedback iterative coherent Itanium machine provided by the invention also has the following characteristics: wherein, step S1 further includes: obtaining a structural feature matrix A of the chemical molecule(l)And combining the node matrix X(l)And the structural feature matrix A(l)Inputting the data into a convolution first layer of a graph convolution neural network to obtain a convolved first structural feature matrix, wherein the expression of the first structural feature matrix is as follows:
A(l+1)＝ReLU(T(l)X(l)W(l))
A(l+1)for the first structural feature matrix, ReLU is the activation function, T(l)For a structural feature matrix A(l)Normalized matrix, X(l)Is a node matrix, W(l)In order to be a weight matrix, the weight matrix,
Figure BDA0003496678610000041
the graph network method based on the self-feedback iterative coherent Isaic machine, provided by the invention, also has the following characteristics that: the expression of the isooctane Hamilton quantity of the self-feedback iterative coherent isooctane machine is as follows:
Figure BDA0003496678610000042
siis an Isinum spin with a value of + -1 corresponding to two states of each node, JijIs the strength of the interaction between two nodes.
The graph network method based on the self-feedback iterative coherent Itanium machine provided by the invention also has the following characteristics: wherein the light field XlAnd a corresponding feedback signal flThe updating is carried out through two stages, namely a sampling stage and a processing stage, and the L-th light field in the coupled light field isThe time evolution equation in the kth iteration process is as follows:
Figure BDA0003496678610000043
ζl[k]is a noise term, fl[k]Is a feedback term.
The graph network method based on the self-feedback iterative coherent Itanium machine provided by the invention also has the following characteristics: wherein f isl[k]The expression of (a) is as follows:
Figure BDA0003496678610000051
fl[k]both for each light field xl[k]Also includes a coupling matrix of Jijα' is the feedback strength and β represents the coupling strength.
The graph network method based on the self-feedback iterative coherent Itanium machine provided by the invention also has the following characteristics: let the Lth in-phase component measured at the kth round trip be recorded as
Figure BDA0003496678610000052
The corresponding feedback signal is
Figure BDA0003496678610000053
The expression for the sampling phase is as follows:
Figure BDA0003496678610000054
wherein
Figure BDA0003496678610000055
Is the phase difference between the phase difference and the phase difference,
Figure BDA0003496678610000056
beta represents the strength of the coupling and,
Figure BDA0003496678610000057
Figure BDA0003496678610000058
feedback signal
Figure BDA0003496678610000059
The expression of (a) is as follows:
Figure BDA00034966786100000510
Figure BDA00034966786100000511
a feedback signal is added to the in-phase component after each round trip.
The graph network method based on the self-feedback iterative coherent Itanium machine provided by the invention also has the following characteristics: the processing stage is that the signals are demultiplexed and matrix multiplication is carried out to complete the coupling between the spin of Isn.
Action and Effect of the invention
According to the graph network method based on the self-feedback iterative coherent Italic machine, provided by the invention, the graph network algorithm is realized on the basis of the Italic algorithm, namely, a spin matrix of an Italic model is mapped onto a node matrix of the graph network, and finally, the Italic algorithm is used for solving the combination optimization problem. The Isci machine consists of an optical path and an electric path, wherein the optical path is responsible for nonlinear operation, and the electric path realizes discrete time feedback operation by sampling optical voltage and feeding the optical voltage back to the Mach-Zehnder modulator, so that the Isci algorithm and the graph network algorithm are combined, the characteristics of parallel processing, low power consumption and the like of the graph network are increased, and the Isci machine can be used for processing specific problems.
Further, the Esin machine is an artificially designed physical system, consisting of a set of artificial "spins" with two-body interactions, and the Hamiltonian of this system can be described by the Esin model. Because the physical system always evolves to the energy lowest state automatically, the Itanium machine also evolves dynamically and is finally stabilized at the ground state of the Itanium model, and the final state provides the optimal solution of the combinatorial optimization problem according to the one-to-one correspondence between the Itanium model and the combinatorial optimization problem. The optical Itanium machine benefits from the advantages of parallelism, expandability, low power consumption and the like of an optical system, so that the computing performance of the optical Itanium machine is superior to that of a traditional electronic computer.
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FIG. 1 is a flow diagram of a graph network method based on a self-feedback iterative coherent Itanium machine in an embodiment of the invention;
FIG. 2 is a block diagram of a self-feedback iterative coherent Icin machine in an embodiment of the present invention;
FIG. 3 is a block diagram of a signal feedback unit according to an embodiment of the present invention;
fig. 4 is a diagram illustrating the operation of a self-feedback iterative coherent machine according to an embodiment of the present invention.
Detailed Description
In order to make the technical means, the creation features, the achievement purposes and the effects of the invention easy to understand, the following describes the graph network method based on the self-feedback iterative coherent machine specifically with reference to the embodiment and the attached drawings.
< example >
FIG. 1 is a flow chart of a graph network method based on a self-feedback iterative coherent Itanium machine in an embodiment of the invention.
As shown in fig. 1, the graph network method based on the self-feedback iterative coherent yixinji provided by the present invention includes the following steps:
step S1, a node matrix of the chemical molecule is obtained.
In this embodiment, a node matrix X of chemical molecules is obtained(l)And structural feature matrix A(l)And combining the node matrix and the structural feature matrix A(l)Inputting the data into a convolution first layer of a graph convolution neural network to obtain a convolved first structural feature matrix, wherein the expression of the first structural feature matrix is as follows:
A(l+1)＝ReLU(T(l)X(l)W(l))
A(l+1)for the first structural feature matrix, ReLU is the activation function, T(l)For a structural feature matrix A(l)Normalized matrix, X(l)Is a node matrix, W(l)In order to be a weight matrix, the weight matrix,
Figure BDA0003496678610000071
step S2, the spin matrix of the self-feedback iterative coherent Eschen model is mapped to the node matrix of the graph network.
The specific mapping process is as follows: the spin matrix of a self-feedback iterative coherent Eschen model (hereinafter referred to as an Eschen model) is mapped to a node matrix of a graph network, each spin in the spin matrix corresponds to a corresponding node in the node matrix, the spin direction of the corresponding node is represented by 1 in the spin matrix, the spin direction is represented by 0, and 1 and 0 respectively represent two different states of each node. Determining whether two corresponding nodes of the graph network node matrix are connected or not by the interaction strength of two adjacent spins in the spin matrix; if the interaction intensity of two adjacent spins is greater than 0, two corresponding adjacent nodes are mutually connected, and the spins of the two nodes are in the same state; if the interaction strength of two adjacent spins is less than 0, the two nodes corresponding to the two adjacent spins are not connected to each other, and the spins of the two nodes are in opposite states.
FIG. 2 is a block diagram of a self-feedback iterative coherent Icin machine in an embodiment of the invention.
As shown in fig. 2, the self-feedback iterative coherent itu machine 100 in the embodiment of the present invention includes a compressed laser generating unit 11, a modulator unit 12, and a signal feedback unit 13.
The compression laser generating unit 11 is a laser for generating a laser beam and injecting a compression vacuum into the laser beam to form a laser beam with compression vacuum injection.
The modulator unit 12 introduces laser with compressed vacuum injection into the modulator unit 12, so that the input compressed optical field is divided into two parts and coupled with the modulator unit, and discrete time feedback operation is realized by sampling optical voltage. In the present embodiment, the modulator unit 12 is a mach-zehnder modulator 131, and in other embodiments, the modulator unit 12 may be an FPGA.
Fig. 3 is a block diagram of a signal feedback unit in an embodiment of the present invention.
As shown in fig. 3, the signal feedback unit 13 includes a mach-zehnder modulator 131, a photodiode 132, an analog-to-digital converter 133, a matrix multiplier 134, a digital-to-analog converter 135, and a phase modulator 136.
The mach-zehnder modulator 131 is configured to modulate optical state information by encoding light intensity after a laser beam with compressed vacuum injection is introduced into the mach-zehnder modulator 131, the input compressed optical field is divided into two parts inside the mach-zehnder modulator, and an output optical signal passes through the signal feedback unit 13 and then couples a plurality of output optical fields together in an optical and electrical manner to generate a bistable optical network capable of representing Ising spin set.
The Photodiode (PD)132 is used to detect the signal output from the mach-zehnder modulator 131 after passing through the PSA ring fiber cavity 14.
An analog-to-digital converter (ADC)133 is used for converting the signal detected by the photodiode 132 into a digital signal.
The matrix multiplier 134 is used for performing corresponding matrix multiplication on the digital signal output by the analog-to-digital converter 133.
A digital-to-analog converter (DAC)135 converts the digital signal of the sampled optical voltage into an optical signal.
The phase modulator 136 is used to set the phase difference corresponding to the feedback signal, the output of which is the square of the in-phase component of the coupled optical field.
Fig. 4 is a diagram illustrating the operation of a self-feedback iterative coherent machine according to an embodiment of the present invention.
As shown in fig. 4, in the self-feedback iterative coherent ising machine 100 provided by the present invention, a laser beam with a compressed vacuum injection is first generated by a compressed laser generating unit 11, and then introduced into the mach-zehnder modulator 131, the modulator 131 effects modulation of the relevant optical state information by encoding the light intensity, the input compressed optical field is divided into two parts by the inner part, the output signal passes through the PSA annular optical fiber cavity 14 and is detected by the photodiode 132, the digital signal is obtained by the analog-to-digital converter 133, and then the matrix multiplier 134 performs corresponding calculation, and discrete time feedback operation is realized by sampling the photovoltage, then, after passing through the digital-to-analog converter 135, the phase modulator 136 on the arm of the mach-zehnder modulator 131 sets the phase difference corresponding to the feedback signal for phase modulation, so that the output signal is the square of the in-phase component of the coupled optical field. Finally, the multiple output optical fields are optically and electrically coupled together to generate a bi-stable optical network that can represent the Ising spin set.
In this embodiment, the expression of the isooctane Hamiltonian of the self-feedback iterative coherent isooctane machine is as follows:
Figure BDA0003496678610000101
siis an Isn spin, has a value of + -1, and corresponds to two states of each node, JijIs the strength of the interaction between two nodes.
For a coupled light field set with discrete time feedback, the time evolution equation of the L light field in the k iteration process is as follows:
Figure BDA0003496678610000102
ζl[k]is a noise term, fl[k]As a feedback term, fl[k]The expression of (a) is as follows:
Figure BDA0003496678610000103
fl[k]both for each light field xl[k]Also includes a coupling matrix of Jijα' is the feedback strength and β represents the coupling strength. In the absence of mutual coupling (β ═ 0), it was found by linear stability analysis that the system occurred when α ═ 1A bifurcation phenomenon is caused. Below the bifurcation point, the system is only in
Figure BDA0003496678610000104
A stable fixed point is arranged; above the bifurcation point, the system has two stable fixed points
Figure BDA0003496678610000105
And an unstable fixation point
Figure BDA0003496678610000106
The bifurcation phenomenon will result in a symmetric bistability, and when the initial system is at an unstable fixed point, a single light field evolving over time will appear with the same probability at one of the two stable points above the bifurcation point. Through sigmal＝sigl(xl[k]) And, an ising spin.
In this embodiment, a time-division multiplexing scheme is employed to facilitate the generation and coupling of multiple optical fields. For a network containing n spins, the feedback signal is divided into n equal intervals, where each interval represents an individual spin. A hybrid calculation scheme is adopted, namely multiplexing and coupling of the light fields are realized by using digital hardware, and nonlinear operation of the system is completed by depending on an optical module.
In each iteration, the light field xlAnd a corresponding feedback signal flThe updating is carried out through two stages, namely a sampling stage and a processing stage. In the sampling phase, multiple feedback signals are injected into the mach-zehnder modulator from the digital-to-analog converter 142(DAC) and the resulting optical field is sampled using the analog-to-digital converter 141 (ADC). In the processing phase, the signals are demultiplexed and a matrix multiplication operation is performed to complete the coupling between Ising spins. The resulting feedback signal is then multiplexed again for the next iteration.
The Lth in-phase component measured at the kth round trip is denoted as
Figure BDA0003496678610000111
The signal is then used to generate a corresponding feedback signal
Figure BDA0003496678610000112
And reinjecting the mixed solution into the Mach-Zehnder modulator to generate a coupling network, wherein the expression of the sampling stage is as follows:
Figure BDA0003496678610000113
wherein
Figure BDA0003496678610000114
Is the phase difference, beta represents the coupling strength, since the phase difference
Figure BDA0003496678610000115
Figure BDA0003496678610000116
Therefore, the first and second electrodes are formed on the substrate,
Figure BDA0003496678610000117
accordingly, the electric field amplitude is positive or negative, and the feedback signal
Figure BDA0003496678610000118
The expression of (a) is as follows:
Figure BDA0003496678610000119
Figure BDA00034966786100001110
a feedback signal is added to the in-phase component after each round trip.
Effects and effects of the embodiments
According to the graph network method based on the self-feedback iterative coherent Italic machine, the graph network algorithm is realized on the basis of the Italic algorithm, namely, a spin matrix of an Italic model is mapped to a node matrix of the graph network, and finally, the Italic algorithm is used for solving the combination optimization problem. The Isci machine consists of an optical path and an electric path, wherein the optical path is responsible for nonlinear operation, and the electric path realizes discrete time feedback operation by sampling optical voltage and feeding the optical voltage back to the Mach-Zehnder modulator, so that the Isci algorithm and the graph network algorithm are combined, the characteristics of parallel processing, low power consumption and the like of the graph network are increased, and the Isci machine can be used for processing specific problems.
Further, the Esin machine is an artificially designed physical system, consisting of a set of artificial "spins" with two-body interactions, and the Hamiltonian of this system can be described by the Esin model. Because the physical system always evolves to the energy lowest state automatically, the Itanium machine also evolves dynamically and is finally stabilized at the ground state of the Itanium model, and the final state provides the optimal solution of the combinatorial optimization problem according to the one-to-one correspondence between the Itanium model and the combinatorial optimization problem. The optical Itanium machine benefits from the advantages of parallelism, expandability, low power consumption and the like of an optical system, so that the computing performance of the optical Itanium machine is superior to that of a traditional electronic computer.

Claims (10)

1. A graph network method based on a self-feedback iterative coherent Itanium machine is used for predicting chemical bond breaking and is characterized by comprising the following steps:
acquiring a node matrix of the chemical molecules;
mapping a spin matrix of a self-feedback iterative coherent Eschen model to the node matrix;
and obtaining the optimal decomposition product of the chemical molecule by a self-feedback iterative coherent Isci machine.
2. The self-feedback iterative coherent Itanium machine-based graph network method according to claim 1, characterized in that:
each spin in the spin matrix corresponds to a corresponding node of the node matrix, and each spin has two spin directions and corresponds to two different states of each node;
the interaction strength of two adjacent spins in the spin matrix determines whether two adjacent nodes of the node matrix are connected or not;
if the interaction intensity of two adjacent spins is greater than 0, two corresponding adjacent nodes are mutually connected, and the spins of the two nodes are in the same state;
if the interaction strength of two adjacent spins is less than 0, two nodes corresponding to the two adjacent spins are not connected to each other, and the spins of the two nodes are in opposite states.
3. The self-feedback iterative coherent yixin machine-based graph network method according to claim 1, characterized in that:
wherein, the self-feedback iterative coherent Icin machine comprises:
the compressed laser generating unit is used for injecting compressed vacuum into the laser to form a laser beam with compressed vacuum injection;
the modulator unit is used for dividing a compressed state light field into two parts and coupling the two parts with the modulator unit, and discrete time feedback operation is realized by sampling photovoltage;
the signal feedback unit is used for detecting an output signal modulated by a feedback signal through the modulator by a photodiode after passing through a PSA annular optical fiber cavity, obtaining a digital signal through an analog-to-digital converter, performing corresponding calculation by a matrix multiplier, realizing discrete time feedback operation by sampling optical voltage, and performing phase modulation by a phase modulator after passing through the digital-to-analog converter so that the output feedback signal is the square of the in-phase component of a coupling optical field.
4. The self-feedback iterative coherent Itanium machine-based graph network method according to claim 3, characterized in that:
wherein the modulator unit is a Mach-Zehnder modulator.
5. The self-feedback iterative coherent Itanium machine-based graph network method according to claim 1, characterized in that:
wherein, step S1 further includes:
obtaining a structural feature matrix A of the chemical molecule(l)And combining the node matrix X(l)And the structural feature matrix A(l)Inputting the data into a convolution first layer of a graph convolution neural network to obtain a convolved first structural feature matrix, wherein the expression of the first structural feature matrix is as follows:
A(l+1)＝ReLU(T(l)X(l)W(l))
A(l+1)for the first structural feature matrix, ReLU is the activation function, T(l)For the structural feature matrix A(l)Matrix to be normalized, X(l)Is said node matrix, W(l)In order to be a weight matrix, the weight matrix,
Figure FDA0003496678600000031
6. the self-feedback iterative coherent Itanium machine-based graph network method according to claim 1, characterized in that:
wherein, the expression of the isooctane Hamilton quantity of the self-feedback iterative coherent isooctane machine is as follows:
Figure FDA0003496678600000032
siis an Isinum spin with a value of + -1 corresponding to two states of each node, JijIs the strength of the interaction between the two nodes.
7. The self-feedback iterative coherent Isci machine-based graph network method according to claim 4, wherein:
wherein the light field XlAnd a corresponding feedback signal flUpdating through two stages, namely a sampling stage and a processing stage, wherein the time evolution equation of the L-th optical field in the coupled optical field in the k-th iteration process is as follows:
Figure FDA0003496678600000033
ζl[k]is a noise term, fl[k]Is a feedback term.
8. The self-feedback iterative coherent Itanium machine-based graph network method of claim 7, wherein:
wherein f isl[k]The expression of (a) is as follows:
Figure FDA0003496678600000041
fl[k]both for each light field xl[k]Self-feedback, also including coupling matrices of Jijα' is the feedback strength and β represents the coupling strength.
9. The self-feedback iterative coherent Itanium machine-based graph network method of claim 7, wherein:
let the Lth in-phase component measured at the kth round trip be recorded as
Figure FDA0003496678600000042
The corresponding feedback signal is
Figure FDA0003496678600000043
The expression of the sampling phase is as follows:
Figure FDA0003496678600000044
wherein
Figure FDA0003496678600000045
Is the phase difference between the phase difference and the phase difference,
Figure FDA0003496678600000046
beta represents the strength of the coupling and,
Figure FDA0003496678600000047
feedback signal
Figure FDA0003496678600000048
The expression of (c) is as follows:
Figure FDA0003496678600000049
Figure FDA00034966786000000410
a feedback signal is added to the in-phase component after each round trip.
10. The self-feedback iterative coherent Itanium machine-based graph network method of claim 7, wherein:
and the processing stage is to demultiplex the signals and perform matrix multiplication to complete the coupling between the spin numbers.
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CN117130428B (en) * 2022-12-02 2024-04-19 上海交通大学 NP complete problem implementation method based on programmable photon chip
CN115858999A (en) * 2023-02-07 2023-03-28 华南理工大学 Combined optimization problem processing circuit based on improved simulated annealing algorithm
CN115858999B (en) * 2023-02-07 2023-04-25 华南理工大学 Combined optimization problem processing circuit based on improved simulated annealing algorithm

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