CN107295526B - Stable matching algorithm-based frequency spectrum allocation method for ensuring lower limit of demand - Google Patents
Stable matching algorithm-based frequency spectrum allocation method for ensuring lower limit of demand Download PDFInfo
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Abstract
The invention relates to a frequency spectrum allocation method for ensuring a demand lower limit based on a stable matching algorithm, which is characterized in that the number of frequency spectrums which need to be reserved for meeting the demand lower limit of all buyers and the number of frequency spectrums which can be freely controlled are calculated according to the minimum frequency spectrum demand, budget cost and interference relation of frequency spectrum buyers, an improved matching algorithm of a deferred acceptance mode is operated on the basis, a stable frequency spectrum allocation result is achieved, the frequency spectrum allocation result is ensured to meet the minimum frequency spectrum demand and cost budget of a secondary user, and the success rate and satisfaction degree of frequency spectrum transaction of a primary user and the secondary user are improved.
Description
Technical Field
The invention belongs to the technical field of computer networks, and particularly relates to a frequency spectrum allocation model for ensuring a lower limit of demand based on a stable matching algorithm.
Background
In the current internet era, the spectrum of wireless communication networks is an essential resource. However, due to the increasing amount of wireless communication traffic, spectrum is also becoming a tight resource. In order to make the best possible use of the existing spectrum and to avoid the waste of spectrum due to the conventional static spectrum allocation method. The dynamic spectrum allocation method is born, and can enable a wireless communication service provider to buy and sell surplus spectrum channels according to the requirement of the wireless communication service provider.
Trading activity of spectrum is essentially a match between spectrum buyers and sellers. The stable spectrum matching result is a reasonable matching result for the free spectrum trading market with respect to the optimal spectrum matching result. The reason is as follows: (1) both buyers and sellers in the trading market are selfish, considering only maximizing their own interests, which is not strictly consistent with the goal of optimization of the overall trading system. The optimal matching algorithm can be forcibly executed only in a centralized system with a controller, and the stable matching algorithm considers the personal preference of buyers and sellers, so that any buyer or seller can unilaterally obtain a better matching result, and the implementation of the matching algorithm in a distributed free spectrum transaction market is ensured. (2) From a computational complexity point of view, the optimal matching scheme tends to be NP-hard, while the stable spectral matching method can be solved in polynomial time.
A stable matching algorithm was derived from studies by Gale and sharley et al. They have originally proposed a Deferred Acceptance (DA) algorithm to solve the matching problem with the requirement upper limit. The deferred acceptance algorithm is widely applied to the problem of resource allocation in the field of computer science, such as cloud virtual machine management, user access in a home base station, end-to-end spectrum sharing and the like.
Unlike the traditional matching problem, spectrum allocation has an important characteristic of reusability. The reusability means that signals of two users far enough away do not interfere with each other due to signal attenuation in the wireless communication process, so that the two users can use the same frequency spectrum. Similarly, in the spectrum trading market, a spectrum seller can be allowed to sell its spectrum to a buyer which is far enough away that signals do not interfere with each other. Spectrum reuse improves spectrum use efficiency, but presents challenges to the design of stable spectrum matching algorithms. Chen et al have proposed an adaptive two-stage desired acceptance algorithm that takes advantage of spectrum reusability and gives stable matching results. However, this algorithm only considers the upper spectral demand limit for each buyer. In fact, to achieve proper operation of wireless communications, spectrum buyers also have a lower limit on their spectrum demand. The traditional delay acceptance algorithm cannot meet the requirement lower limit, and D.Fragiadakis provides an expanded delay acceptance algorithm for solving the problem of matching of the requirement upper limit and the requirement lower limit. However, due to the characteristic of reusability of the spectrum, the algorithm cannot be directly used for solving the spectrum matching problem.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a frequency spectrum allocation model for ensuring the lower limit of the demand based on a stable matching algorithm.
The technical scheme of the invention is a frequency spectrum allocation model for ensuring the lower limit of the demand based on a stable matching algorithm, which comprises the following steps:
a frequency spectrum allocation method for guaranteeing a lower limit of demand based on a stable matching algorithm is characterized in that P frequency spectrum buyers and Q frequency spectrum sellers are defined, the frequency spectrum buyers are secondary users and the frequency spectrum sellers are primary users, and the method comprises the following steps:
step 1, establishing Q interference graphs, wherein each interference graph corresponds to the frequency spectrum of a frequency spectrum seller, namely establishing an interference graph G for the frequency spectrum seller ss＝(N,Es) Wherein the node set N is a set of P spectrum buyers and the edge set EsThe establishment is as follows. For each pair of spectrum buyers j, j ', if j, j' interferes on spectrum s, edges are added
Set of edges EsIn (1). Step 2, establishing a preference relationship between the buyer and the seller and a preference relationship between the seller and the buyer set according to the frequency spectrum bid of the frequency spectrum buyer and the frequency spectrum of the frequency spectrum seller, wherein the specific method comprises the following steps: the preference relationship between the buyer and the seller is generated by the method that if the bidding relationship between the buyer i and the seller j' is
Then the preference relationship is j > i j'. The seller's preference relationship to the buyer's collection is determined by the buyer's bid and interference map decision. Assuming that there are buyer sets A and B for seller i, if none of the buyers in buyer set A interfere with each other, i.e. the system and method for the system and method
The buyers in the seller set B interfering with each other, i.e.
Then the preference relationship is A >iB; if neither buyer in buyer set A nor buyer in set B interfere with each other, and the total bid of the buyer in A is higher than the total bid of the buyer in B, i.e.
Then the preference relationship is A >iB, and vice versa;
step 3, calculating the disposable frequency spectrum number theta, and the specific steps are as follows:
step 3.1, lower limit for each demand is pcBuyer s, creating pcAnd a virtual node.
And 3.2, each newly-built virtual node inherits all interference relationships of the original node, namely inherits the edges of the original node in all original interference graphs.
And 3.3, creating conflict edges between every two virtual nodes of the same original node.
And 3.4, calculating the minimum color number, namely M-color, which can cover the whole G, of the interference graph obtained in the steps 3.1 to 3.3 by using a Welch Powell method, wherein M is the number of all sellers.
step 4.1, caAnd cbInheriting the conflict relationship of all c, i.e. inheriting the edge of c in the original interference graph.
Step 4.2 at caAnd cbAn edge is established between them.
Step 5, matching frequency spectrums, and specifically comprises the following steps;
step 5.1, listing candidate matching objects A of all sellers sSIs set as the overall buyer N. List W of candidate matching objects of all buyers ccSet as the empty set. The final matching lists μ (c) of all buyers and μ(s) of all sellers are set as an empty set.
Step 5.2, if the candidate matching object column of the seller existsTABLE ASIf not, skipping to step 5.3; otherwise, the entire algorithm ends.
Step 5.3, list A of all candidate matching objectsSVendors s that are not empty collections use a greedy algorithm on their interference graph GsUpper solved maximum independent set
Step 5.4, if all the sellers s are determined according to step 5.23
If all are empty sets, ending the step 5; otherwise, jump to step 5.5.
Step 5.5, extremely Large independent set for all sellers sBuyer c in (1), add s to the candidate matching object list W of ccPerforming the following steps; list of candidate matching objects from sSDeleted in (1), and in the conflict graph G of ssWherein the node representing c and the edges connected to it are deleted.
Step 5.6, list W of all candidate matching objectscBuyer c, who is not empty, proceeds to the following process:
step 5.61, if c belongs to a conventional buyer, at WcAnd mu (c), selecting the frequency spectrums which are preferably not more than the requirement upper limit number of c and are preferred by c as new mu (c) in the union set, adding c into a matching list mu(s) of the frequency spectrums, and skipping to the step 5.7; otherwise, if c belongs to the expanded buyer, let the temporary count variable count be 0, and jump to step 5.62.
Step 5.62, when the count is less than the number theta of the disposable spectrums, and the expandable buyer c meets the requirement upper limit that the modulus of the mu (c) is less than the c and the candidate matching object list W of the c existscAnd when the set is not an empty set, sequentially considering the matching frequency spectrum of the buyer c, otherwise, skipping to the step 5.7. Consider buyer ciIf μ (c)i) Is less than ciUpper limit of demand of (c)iCandidate (a) ofMatching object listNot empty set, from
And μ (c)i) C in the union ofiThe best spectrum s is added to mu (c)i) And c isiAdding s from the matching list μ(s) of spectrum s
Deleting and generating an interference pattern GsIn represents ciDeleting the node and the edge connected with the node, and adding 1 to the count variable count; otherwise, if μ (c)i) Is equal to ciUpper limit of demand or ciCandidate matching object list of
If not, i is i +1, and repeat step 5.62.
Step 5.7, emptying Wc。
Step 5.8 jumps to step 5.2.
In the above-mentioned spectrum allocation method based on the guaranteed demand lower limit of the stable matching algorithm,
in step 3, the Welch Powell algorithm includes:
and 2.1, arranging the nodes in the interference graph G according to the descending order of degrees (the nodes with the same degree are arranged randomly).
And 2.2, coloring the first node by using the first color, and coloring each point which is not adjacent to the previous node by the same color according to the arrangement order.
Step 2.3, repeat step 2.2 for the not yet colored dots with the second color until all dots are colored.
And 2.4, the required color number is coloring. The number of freely available frequency spectra is θ ═ M-ranging.
The above-mentioned guarantee requirement based on stable matching algorithmThe spectrum allocation method for solving the lower limit is used for calculating and solving the maximum independent set in step 5
The greedy algorithm of (a) comprises:
step 5.1, for all sellers s, find out the buyer set Qs. At QsThe buyer in (1) satisfies the constraint:
constraint 1 in candidate matching object list ASPerforming the following steps;
constraint 2, does not interfere with any buyer c in the matching list μ(s).
Step 5.2,As an interference pattern GsIs composed of QsSubgraph of buyer, to
Node n, weight innIs the weight of node n, degreenDegree of node n, according to weightn/(degreen+1) sort the nodes in descending order.
Step 5.3, take out the node n arranged at the front, namely weightn/(degreen+1) the node with the largest value, adding it to the largest independent set
From (1) it is selected
Delete and remove all nodes and edges connected to it from
Is deleted.
Step 5.4, when
When the node does not exist any more, the algorithm is ended; otherwise, jump to step 5.2.
The invention has the following advantages: the spectrum allocation method described by the invention can meet the spectrum demand lower limit and cost budget of all spectrum buyers, and ensure the stability of the spectrum allocation result, namely, no pair of spectrum buyers and sellers hope to mutually replace the currently matched spectrum sellers and buyers. The frequency spectrum allocation method has high operation efficiency and polynomial complexity. Compared with the traditional spectrum allocation method, the final spectrum allocation result obtained by the method improves the transaction success rate and satisfaction degree of the spectrum buyer and the spectrum seller.
Drawings
Fig. 1 is an algorithm flow diagram of the spectrum matching method of the present invention.
Fig. 2a is a spectrum matching flow chart (first round) of an embodiment of the invention.
Fig. 2b is a spectrum matching flow chart (second round) of an embodiment of the invention.
Fig. 2c is a spectrum matching flow chart (third round) of an embodiment of the present invention.
Fig. 2d is a spectrum matching flow chart (final matching result) of the embodiment of the present invention.
FIG. 3 is a flow chart of the Welch Powell algorithm of the present invention.
FIG. 4 is the largest independent set of the present invention
Greedy algorithm flow diagram of (1).
Fig. 5 is a schematic diagram of the relationship of the interference pattern assumed by the secondary user (spectrum buyer) on each spectrum in the embodiment of the present invention.
Fig. 6 is a schematic relationship diagram after 2, 1, and 2 virtual nodes are created for three buyers in the embodiment of the present invention.
FIG. 7 is an interference graph after generation of regular and extended buyers in an embodiment of the present invention.
Detailed Description
The invention provides a spectrum allocation model for ensuring the lower limit of the demand based on a stable matching algorithm, which is mainly based on an extended delay algorithm meeting the lower limit of the demand and considers the characteristic of spectrum reusability. The method fully considers the matching success rate and the satisfaction degree of the buyer and the seller. The spectrum allocation result obtained by the invention can be suitable for the spectrum market with free spectrum trading.
The method provided by the invention can realize the process by using a computer software technology. Referring to fig. 1, the embodiment is a specific illustration of the process of the present invention, and the embodiment is as follows:
suppose there are three spectrum buyers a, B, C, six spectrum sellers a, B, C, d, e, f, each having a spectrum. The bids of spectrum buyers on the spectrum sellers are shown in the following table.
Table 1.
| Buyer A | Buyer B | Buyer C | |
| Seller a | 6 | 1 | 1 |
| |
4 | 2 | 3 |
| Seller c | 2 | 6 | 5 |
| Seller d | 1 | 3 | 4 |
| Seller e | 5 | 5 | 2 |
| Seller f | 3 | 4 | 6 |
| Lower limit of demand | 2 | 1 | 2 |
| Upper limit of demand | 3 | 3 | 3 |
Step 1, establishing an interference graph G according to the interference relation of the secondary users transmitted on the frequency spectrum of each primary users＝(N,Es) Where the set of nodes N represents all secondary users. If secondary users c and c' interfere on spectrum s, edges are added
Set of edges EsIn (1).
In the embodiment, it is assumed that the interference pattern of the secondary users (spectrum buyers) on each spectrum is the same, as shown in fig. 5.
And 2, establishing a preference relationship of the buyer to the seller and a preference relationship of the seller to the buyer set according to the bid of the secondary user (the spectrum buyer) on the spectrum of the primary user (the spectrum seller).
The preference relationship between the buyer and the seller is generated by the method that if the bidding relationship between the buyer i and the seller j' isThen the preference relationship is j > i j'. The seller's preference relationship to the buyer's collection is determined by the buyer's bid and interference map decision. Assuming that there are buyer sets A and B for seller i, if none of the buyers in buyer set A interfere with each other, i.e. the system and method for the system and method
The buyers in the seller set B interfering with each other, i.e.
Then the preference relationship is A > i B; if neither buyer in buyer set A nor buyer in set B interfere with each other, and the total bid of the buyer in A is higher than the total bid of the buyer in B, i.e.
Then the preference relationship is A > i B and vice versa.
The specific embodiments of the examples are as follows:
according to the bid of the buyer to the seller, the preference relationship of the buyer to the seller can be established as follows:
a＞＞Ae＞＞Ab＞＞Af＞＞Ac＞＞Ad
c＞＞Be＞＞Bf＞＞Bd＞＞Bb＞＞Ba
f＞＞Cc＞＞Cd＞＞Cb＞＞Ce＞＞Ca
step 3, calculating the disposable frequency spectrum number theta, and the specific steps are as follows: (1) the lower limit for each demand is pcBuyer s, creating pcAnd a virtual node. (2) Each newly-built virtual node inherits all interference relationships of the original node, namely inherits the edges of the original node in all original interference graphs. (3) A conflict edge is created between every two virtual nodes of the same original node. (4) Using the Welch Powell method, the interference patterns obtained in steps (1), (2) and (3) are calculated to obtain the minimum color number ranging, θ -M-ranging, which can cover the whole G, where M is the number of all vendors.
The Welch Powell algorithm can be described as follows:
(1) the nodes in the interference graph G are arranged in descending order of degrees (the arrangement of the nodes of the same degree is random).
(2) The first node is colored with a first color and each point that is not adjacent to the preceding node is colored in rank order with the same color.
(3) Repeating (2) for the as-yet uncolored dots with the second color until all of the dots are colored.
(4) The number of colors required is coloring.
The specific embodiments of the examples are as follows:
since the minimum matching numbers of a, B, and C are 2, 1, and 2, respectively, 2, 1, and 2 virtual nodes, i.e., a ', B, C, and C', are created for three buyers, respectively. Each newly-built virtual node inherits all interference relationships of the original node, namely inherits the edges of the original node in all original interference graphs. A conflict edge is created between every two virtual nodes of the same original node. As shown in fig. 6.
In a graph formed by virtual nodes, a Welch Powell method is used to calculate the minimum color number ranking capable of covering the whole graph, and the specific process is as follows:
(1) and sorting the nodes in the conflict graph according to the descending order of degrees, wherein the sorting result is A, A ', C, C' and B.
(2) Coloring A with color 1 and coloring nodes not connected with A. Since all nodes are connected to a, color 1 can only color a. Similarly, a' is colored with color 2. C and node B not connected to C are colored with color 3, and C' is colored with color 4. And finishing coloring all the virtual nodes. 4 colors were used.
(3)θ＝6-4＝2。
Step 3, according to the requirement lower limit p of each buyer ccAnd a demand upper limit qc(determined by buyer budgets), two new virtual buyers are generated: conventional type caAnd expanded form cb。caHas a lower demand limit of 0 and an upper demand limit of pc；cbHas a lower demand limit of 0 and an upper demand limit of qc-pc。caAnd cbInherit the bid and preference relationships of c to all sellers. Establishing a new interference graph G by taking all new virtual buyers as nodes for the frequency spectrums of all sellerssThe method comprises the following specific steps: (1) c. CaAnd cbInheriting the conflict relationship of all c, i.e. inheriting the edge of c in the original interference graph. (2) At caAnd cbAn edge is established between them.
The specific embodiments of the examples are as follows:
the generated regular buyers and the extended buyers are as follows: a. thea,Ab,Ba,Bb,Ca,CbThe lower demand limits are all 0, the upper demand limits are 2, 1, 2, 1, respectively, and the new interference graph is shown in fig. 7.
Step 5, matching frequency spectrums, and specifically comprises the following steps;
(1) listing candidate matching objects of all sellers sSIs set as the overall buyer N. List W of candidate matching objects of all buyers ccSet as the empty set. The final matching lists μ (c) of all buyers and μ(s) of all sellers are set as an empty set.
(2) If there is a candidate matching object list A of the sellerSIf not, jumping to (3); otherwise, step 5 is ended.
(3) For all candidate matching object list ASVendors s that are not empty collections use a greedy algorithm on their interference graph GsUpper solved maximum independent set
(4) If it is notOf all the sellers s determined in (3)
If all are empty sets, ending the step 5; otherwise, jump to (5).
(5) Extremely large independent set for all sellers s
Buyer c in (1), add s to the candidate matching object list W of ccPerforming the following steps; list of candidate matching objects from sSDeleted in (1), and in the conflict graph G of ssWherein the node representing c and the edges connected to it are deleted.
(6) For all candidate match lists WcIs not an empty buyer c and,
a) if c belongs to a regular buyer, in WcAnd mu (c), selecting the frequency spectrums which are preferred by c and do not exceed the requirement upper limit number of c as new mu (c) in the union set, adding c into a matching list mu(s) of the frequency spectrums, and jumping to (7); otherwise, if c belongs to the expanded buyer, let the temporary count variable count be 0, and jump to b).
b) When the count is less than the number theta of the disposable spectrum, and the expandable buyer c exists, the requirement upper limit of the module of the mu (c) is less than the c is met, and the candidate matching object list W of the ccAnd when the set is not an empty set, sequentially considering the matching frequency spectrum of the buyer c, and otherwise, jumping to (7). Consider buyer ciIf μ (c)i) Is less than ciUpper limit of demand of (c)iCandidate matching object list of
Not empty set, from
And μ (c)i) C in the union ofiThe best spectrum s is added to mu (c)i) And c isiAdding s from the matching list μ(s) of spectrum sDeleting and generating an interference pattern GsIn represents ciDeleting the node and the edge connected with the node, and adding 1 to the count variable count; otherwise, if μ (c)i) Is equal to ciUpper limit of demand or ciCandidate matching object list ofWhen not empty, i ═ i +1, repeat b).
(7) Emptying Wc。
(8) And (4) jumping to (2).
For computing solving maximal independent sets
The greedy algorithm of (c) is described as follows:
(1) for all sellers s, find a set of buyers Qs. At QsThe buyer in (1) satisfies the condition: a) in the candidate matching object list ASPerforming the following steps; b) without interfering with any buyer c in the matching list μ(s).
(2)
As an interference pattern GsIs composed of QsSubgraph of buyer, to
Node n, weight innIs the weight of node n, degreenDegree of node n, according to weightn/(degreen+1) sort the nodes in descending order.
(3) Fetch the node n that is arranged at the head, namely weightn/(degreen+1) the node with the largest value, adding it to the largest independent set
From (1) it is selected
The deletion is carried out by the user,and slave all nodes and edges connected thereto
Is deleted.
(4) When in use
When the node does not exist any more, the algorithm is ended; otherwise, jump to (2).
As shown in fig. 2, the specific embodiment of the example is as follows:
at this time, entering a matching algorithm, and enabling all buyer virtual nodes Aa,Ab,Ba,Bb,Ca,CbAre added to the candidate matching object list A of the seller a, b, c, d, e, fsIn (1).
In the first round of the matching algorithm, for seller a, due to AaWeight of (1)n/(degreen+1) maximum value, AaIndependent set of maximum rights to join seller a
In (A)aAfter the buyer virtual nodes connected with the buyer virtual nodes are deleted from the interference graph, no nodes exist in the interference graph, and the maximum weight independent set of the seller a is { A }a}. Similarly, for seller b, due to CaWeight of (1)n/(degreen+1) maximum, CaIndependent set of maximum rights to join seller b
And delete node Ca,Aa,Ab,CbTaking out the node B from the rest nodesaIs added to
In the interference graph, there is no node, so far, the maximum weight independent set of the seller b is
In the same wayThe maximum independent set of the remaining sellers is { Ca,Ba}. All sellers propose matching application to buyers with maximum independent right and collect the matching application from ASIn the deletion process, the buyer puts the seller who applies for the candidate matching object list WcAnd the buyer node which made the application is deleted in the own interference graph. Namely seller a to AaApply for, the rest sellers to Ca,BaAnd (5) applying. For AaThe channel number of the proposed application is 1, AaThe upper limit of demand of (A) is 2, since the number of applied sellers is less than the upper limit of demandaAnd receiving a matching application of the seller a. For BaThe number of applied sellers is 5, BaThe upper limit of the demand of (1), B, since the number of the seller who made the application is greater than the upper limit of the demandaAnd accepting the application of the most preferred seller c. For CaThe number of applied sellers is 5, CaThe upper limit of demand of (2), since the number of applied sellers is greater than the upper limit of demand, CaAnd accepting the application of the most preferred seller c and seller f. And emptying the candidate matching lists of all buyers. At this point, the first round of matching is finished.
In the second round of matching algorithm, since channel a has been temporarily associated with AaMatch, thus exclude with A when asking for the most independent set of rights for seller aaAn interfering node. So far, there are no more nodes, and the maximum weight independent set of channel a is an empty set. Similarly, the maximum weight independent set of the seller b is obtained as { Cb,Bb}; the maximum right independent set of the seller c is an empty set; the maximum independent set of the sellers d, e, f is { Cb,Bb}. At this time, Cb,BbIs not empty, θ is 2. For BbSelect the most preferred seller e in the candidate matching list, where count is 1<Theta; for CbSelect the most preferred vendor d in the candidate matching list, where count is 2<Theta. And emptying the candidate matching lists of all buyers. At this point, the second round of matching is finished.
In the third round of matching, the maximum weight independent set of the seller b is { A }aAnd the maximum-weight independent sets of the rest sellers are empty sets. Seller b to AaAnd (5) a matching application is proposed. At this time, seller a temporarily associates with AaMatching, the sum of the number of the applied sellers and the number of the temporarily matched sellers is 2 and is not more than AaUpper limit of demand, therefore AaAnd receiving the application of the seller b.
The matching algorithm ends by this point. The matching result is, AaMatching with sellers a and b; b isaMatching with a seller c; b isbMatching with a seller e; caMatching with sellers c and f; cbMatching with seller d.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.
Claims (2)
1. A frequency spectrum allocation method for guaranteeing a lower limit of demand based on a stable matching algorithm is characterized in that I frequency spectrum buyers and J frequency spectrum sellers are defined, the frequency spectrum buyers are secondary users, and the frequency spectrum sellers are primary users, and the method comprises the following steps:
step 1, establishing J interference graphs, wherein each interference graph corresponds to the frequency spectrum of a frequency spectrum seller, namely establishing an interference graph G for a frequency spectrum seller Jj＝(I,Ej) Wherein the node set is a set of I spectrum buyers and the edge set EjThe establishment method is as follows; for each pair of spectrum buyers i and i ', if i and i' interfere on the spectrum seller j, an edge is added
Set of edges EjPerforming the following steps;
step 2, establishing a preference relationship between the buyer and the seller and a preference relationship between the seller and the buyer set according to the frequency spectrum bid of the frequency spectrum buyer and the frequency spectrum of the frequency spectrum seller, wherein the specific method comprises the following steps: the preference relationship between the buyer and the seller is generated by the method that if the bidding relationship between the buyer i and the seller j' is
Then the preference relationship is j >ij'; the preference relationship of the seller to the buyer set is determined by the bids of the buyers and the interference graph; assuming that there are buyer sets A and B for seller j, if none of the buyers in buyer set A interfere with each other, i.e., all of the buyers in seller set A do not interfere with each other
The buyers in buyer set B are interfering with each other, i.e.
Then the preference relationship is A >jB; if neither buyer in buyer set A nor buyer in set B interfere with each other, and the total bid of the buyer in A is higher than the total bid of the buyer in B, i.e.
Then the preference relationship is A >jB, and vice versa;
step 3, calculating the disposable frequency spectrum number theta, and the specific steps are as follows:
step 3.1, lower limit for each demand is piBuyer i, create piA plurality of virtual nodes;
step 3.2, each newly-built virtual node inherits all interference relationships of the original node, namely inherits the edges of the original node in all original interference graphs;
3.3, creating conflict edges between every two virtual nodes of the same original node;
step 3.4, calculating the minimum color number ranking capable of covering the whole G, and θ ═ J | -ranking by using a Welch Powell method for the interference graph obtained in the step 3.1 to the step 3.3, wherein | J | is the number of all sellers;
step 4, according to the requirement lower limit p of each buyer iiAnd a demand upper limit qiTwo new virtual buyers are generated: conventional type iaAnd expanded type ib；iaThe lower limit of the demand of (2) is 0Upper limit of pi；ibHas a lower demand limit of 0 and an upper demand limit of qi-pi；iaAnd ibInheriting the relation of the bids and the preferences of i to all sellers; establishing a new interference graph G by taking all new virtual buyers as nodes for the frequency spectrums of all sellers jjThe method comprises the following specific steps:
step 4.1, iaAnd ibInheriting the conflict relationship of all i, namely inheriting the edge of i in the original interference graph;
step 4.2, in iaAnd ibAn edge is established between the two edges;
step 5, matching frequency spectrums, and specifically comprises the following steps;
step 5.1, listing candidate matching objects A of all sellers jjSetting as a whole buyer I; list W of candidate matching objects of all buyers iiSetting as an empty set; setting the final matching lists mu (i) of all buyers and the final matching lists mu (j) of all sellers as an empty set;
step 5.2, if the candidate matching object list A of the seller existsjIf not, skipping to step 5.3; otherwise, the whole algorithm is ended;
step 5.3, list A of all candidate matching objectsjSeller j, not an empty set, using greedy algorithm in its interference graph GjUpper solved maximum independent set
For computing solving maximal independent sets
The greedy algorithm of (a) comprises:
step 5.31, for all sellers j, find out buyer set Qj(ii) a At QjThe buyer in (1) satisfies the constraint:
constraint 1 in candidate matching object list AjPerforming the following steps;
constraint 2, no interference with any buyer i in the matching list μ (j);
step 5.32,
As an interference pattern GjIs composed of QjSubgraph of buyer, to
Node n, weight innIs the weight of node n, degreenDegree of node n, according to weightn/(degreen+1) sorting the nodes in descending order;
step 5.33, take out the node n arranged at the top, namely weightn/(degreen+1) the node with the largest value, adding it to the largest independent set
From (1) it is selected
Delete and remove all nodes and edges connected to it fromDeleting;
step 5.34, if
In which there is no more node, the maximum independent set at that time is output
Otherwise, go back to step 5.31;
step 5.4, if all the vendors j found according to step 5.3
If all are empty sets, ending the step 5; otherwise, jumping to step 5.5;
step 5.5, extremely Large independent set for all vendors j
Buyer i in (1), add j to the candidate matching object list W of iiPerforming the following steps; list of candidate matches A for i from jjDeleted in j and conflict graph G in jjDeleting the node representing i and the edge connected with the node;
step 5.6, list W of all candidate matching objectsiBuyer i, who is not empty, proceeds with the following processes:
step 5.61, if i belongs to the conventional buyer, in WiAnd mu (i) selects the frequency spectrum which is the best and does not exceed the requirement upper limit number of i as new mu (i), adds i into the matching list mu (j) of the frequency spectrums, and jumps to step 5.7; otherwise, if i belongs to the expanded buyer, making the temporary count variable count equal to 0, and skipping to step 5.62;
step 5.62, when the count is less than the disposable spectrum number theta, and the expandable buyer i meets the requirement upper limit that the modulus of the mu (i) is less than the i and the candidate matching object list W of the i existsiWhen the set is not an empty set, sequentially considering the matching frequency spectrum of the buyer i, otherwise, skipping to the step 5.7; considering buyer i, if the modulus of μ (i) is less than the demand bound of i and the candidate matching object list W of iiNot empty set, from WiAnd μ (i) adding i to μ (i) and i to the matching list μ (j) of spectrum j, j being W from WiDeleting and generating an interference pattern GjDeleting the node representing i in the list and the edges connected with the node, and adding 1 to a counting variable count; otherwise, if the modulus of μ (i) is equal to the demand upper limit of i or ciIs selected from the list W of candidate matching objectsiIf not, i is i +1, and repeating the step 5.62;
step 5.7, emptying Wi；
Step 5.8 jumps to step 5.2.
2. The method for allocating spectrum based on guaranteed demand lower limit of stable matching algorithm as claimed in claim 1, wherein:
in step 3, the Welch Powell algorithm includes:
step 2.1, arranging the nodes in the interference graph G according to the descending order of degrees;
step 2.2, coloring the first node by using the first color, and coloring each point which is not adjacent to the previous node by the same color according to the arrangement sequence;
step 2.3, repeating step 2.2 for the uncolored points with the second color until all the points are colored;
step 2.4, the required color number is coloring; the number of freely available spectra is θ ═ J | - -ranging.
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