EXHIBIT 2052
`
`12. A method for visually
`displaying data related to a web
`having identifiable web pages
`and Universal Resource
`Locators with pointers,
`compnsmg:
`
`Google's search engine that uses PageRank employs methods for visually
`displaying data relating to the World Wide Web (and other webs) having
`identifiable web pages and URLs with pointers:
`
`Google's search engine that uses PageRank employs methods for visually displaying
`data related to the World Wide Web. Search results including identifiable web pages
`and URLs with pointers are displayed to the user. The user may click on a URL
`provided by Google and request Google to display the full text of the web page.
`Google provides an interface for receiving the inputs, processes the inputs, and sends
`appropriate instructions. Google also automatically displays a portion of the web page
`and in some cases the full text of the web page.
`
`1
`
`
`
`12. A method for visually
`displaying data related to a web
`having identifiable web pages
`and Universal Resource
`Locators with pointers,
`compnsmg:
`
`Google's search engine that uses PageRank employs methods for visually
`displaying data relating to the World Wide Web (and other webs) having
`identifiable web pages and URLs with pointers:
`
`Google's search engine that uses PageRank employs methods for visually displaying
`data related to the World Wide Web. Search results including identifiable web pages
`and URLs with pointers are displayed to the user. The user may click on a URL
`provided by Google and request Google to display the full text of the web page.
`Google provides an interface for receiving the inputs, processes the inputs, and sends
`appropriate instructions. Google also automatically displays a portion of the web page
`and in some cases the full text of the web page.
`
`1
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`Challenged Claims of ’571
`Patent
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`12. A method for visually
`displaying data related to a web
`having identifiable web pages
`and Universal Resource
`Locators with pointers,
`comprising:
`
`EXHIBIT 2052
`
`Evidence of Infringement – Google’s Search Engine that uses PageRank
`
`Google’s search engine that uses PageRank employs methods for visually
`displaying data relating to the World Wide Web (and other webs) having
`identifiable web pages and URLs with pointers:
`
`Google’s search engine that uses PageRank employs methods for visually displaying
`data related to the World Wide Web. Search results including identifiable web pages
`and URLs with pointers are displayed to the user. The user may click on a URL
`provided by Google and request Google to display the full text of the web page.
`Google provides an interface for receiving the inputs, processes the inputs, and sends
`appropriate instructions. Google also automatically displays a portion of the web page
`and in some cases the full text of the web page.
`
`
`
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`Google Search for “Google PageRank”
`
`
`
`choosing an identifiable web
`
`The PageRank algorithm chooses an identifiable web page in order to analyze the link
`structure of the web and calculate a unique PageRank score for the individual web
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`page;
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`page, which determines which web pages are displayed. In doing so, Google selects
`each node and conducts an analysis through mathematical calculation of the link
`structure of the web in relation to that specific selected node to determine a numerical
`score specifically associated with the node or web page.
`
`This is clearly seen in one of the disclosed mathematically equivalent formulations of
`PageRank, where web page A is selected and the analysis is subsequently computed
`with respect to the selected web page A:
`
` “
`
` [T]he rank of a page A is defined according to the present invention as
`
`
`where Bl, ... , Bn are the backlink pages of A, r(Bl), ... , r(Bn ) are their ranks, |B1|, ... ,
`|Bn| are their numbers of forward links, and α is a constant in the interval [0,1], and N
`is the total number of pages in the web. Ex. 2086:’999 Patent, 4:15-25.
`
`Furthermore, these web pages are identified by at least their URL and the unique
`number assigned to it internally by Google:
`
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`“We convert each URL into a unique integer, and store each hyperlink in a
`database using the integer IDs to identify pages.” Ex. 2054: The PageRank Citation
`Ranking: Bringing Order to the Web at 3.1
`
`
`Nodes (documents, webpages, hosts, sites, domains, blogs etc.) existing as or relating
`to webpages residing on the Web (or nodes in a related database) may have direct
`references from one node to another and indirect relationships though a series of
`connected hyperlinks. As part of its clustering analysis and the calculation of its ranks,
`Google’s Software also chooses contributing nodes to analyze for purposes of
`quantifying relationships between the scored nodes and the contributing nodes. An
`analysis unique to the contributing node in relation to the scored node is conducted.
`
`identifying Universal Resource
`Locators for the web pages,
`wherein the identified Universal
`Resource Locators either point
`to or point away from the
`chosen web page;
`
`PageRank identifies Universal Resource Locators which either point to or point
`away from the chosen web page in order to perform link analysis on the chosen
`web page. When a web page is chosen for analysis, the link structure connecting
`the identified web page to other web pages is determined and used to create an
`adapted adjacency matrix for use in the calculation of the PageRank algorithm.
`These matrices map the direct links between each web page on the Web identified
`by Google. Ex. 2099: Langville, Amy and Meyer, Carl D, Google's PageRank and
`
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`Beyond: The Science of Search Engine Rankings, at 31-52 (Princeton University
`Press 2006).
`
`The citation (link) graph of the web is an important resource that has largely
`gone unused in existing web search engines. We have created maps containing
`as many as 518 million of these hyperlinks, a significant sample of the total.
`The Anatomy of a Large-Scale Hypertextual Web Search Engine, at 2.1.
`
`Google’s algorithm uses the identified URLs in its PageRank algorithm to
`calculate the PageRank Scores
`
`The indexer performs another important function. It parses out all the links in
`every web page and stores important information about them in an anchors file.
`This file contains enough information to determine where each link points
`from and to, and the text of the link. … The URLresolver reads the anchors
`file … It also generates a database of links which are pairs of docIDs. The links
`database is used to compute PageRanks for all the documents.
`Ex. 2053: The Anatomy of a Large-Scale Hypertextual Web Search Engine, at
`
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`§4.1 (emphasis added)
`
`See also id. at 4.1 fig.1 (red box added) below:
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`7
`Google identifies URLs by converting the URL string into a docID code:
`
`Additionally, there is a file which is used to convert URLs into docIDs. It is a
`
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`PageRank analyzes Universal Resource Locators including the identified URLs and
`locates URLs which have an indirect relationship with the chosen web page, and
`cluster analyzes the URLs for indirect relationships.
`
`PageRank analyzes URLs including the identified URLs.
`
`Google obtains and stores information concerning the hyperlink structure of the web
`based on the chosen web pages and identified Universal Resource Locators in a link
`database. Google’s Software includes methods of analyzing URLs stored in the
`database of links to build representations of direct relationships between objects (e.g.,
`web page, domain, site, blog, or website). For example, the links database is used to
`create an adapted adjacency matrix for use in the calculation of the PageRank
`algorithm. This algorithm (described in further detail below) analyzes the identified
`URLs by building representations based on the link structure of the identified URLs
`and by calculating the PageRanks of all the documents based on the links database
`which contains information regarding the identified URLs. See limitation directly
`above. These matrices map the direct links between each web page on the Web. Ex.
`2099: Langville, Amy and Meyer, Carl D, Google's PageRank and Beyond: The
`Science of Search Engine Rankings, at 31-52 (Princeton University Press 2006).
`
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`analyzing Universal Resource
`Locators, including the
`identified Universal Resource
`Locators, wherein Universal
`Resource Locators which have
`an indirect relationship to the
`chosen web page are located,
`wherein the step of analyzing
`further comprises cluster
`analyzing the Universal
`Resource Locators for indirect
`relationships; and
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`
`
`PageRank locates URLs which have an indirect relationship with the chosen web
`page.
`
`Google’s PageRank algorithm is a recursive mathematical algorithm that analyze
`portions of the set of direct links for contributions of websites, web pages, and other
`objects that are indirectly linked to the objects being scored. The formula for
`calculating the PageRank of the page, as provided by Ex. 2053: The Anatomy of a
`Large Scale Search Engine, by Brin and Page (1998) is as follows:
`
`We assume page A has pages T1....Tn which point to it (i.e., are citations). The
`parameter d is a damping factor which can be set between 0 and 1. We usually set d to
`0.85. Also C(A) is defined as the number of links going out of page A. The PageRank
`of a page A is given as follows:
`
`PR(A) = (1-d) + d(PR(T1)/C(T1) + .... + PR(Tn)/C(Tn))
`
`The above algorithm, including Google’s subsequent elaborations on the basic
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`formula, is applied recursively and measures contributions from indirectly related
`nodes. See Ex. 2099: Langville, Amy and Meyer, Carl D, Google’s PageRank and
`Beyond: The Science of Search Engine Rankings, at 31-52 (Princeton University Press
`2006).
`
`The above recursive algorithm shows links indirectly related to a node nevertheless
`directly contribute to the PageRank score of that node. By recursively analyzing link
`relationships that are only indirectly related to the selected object, Google’s algorithm
`necessarily locates, identifies, and analyzes URLs which have only an indirect
`relationship with the chosen web page.
`
`PageRank cluster analyzes (i.e., uses cluster links) the URLs for indirect
`relationships
`
`Claim 12 is described in Fig. 14B of the ‘571 patent. An example of cluster analyzing
`is described in step 3012 of Fig. 14B.
`
`The PageRank algorithm analyzes clusters of links (i.e., multiple relationships) within
`a specific path length from a selected web page to generate a PageRank score for the
`
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`selected web page. During each iteration, the algorithm calculates the amount of
`contribution to the PageRank score by nodes of a specific path length. The maximum
`path length described in its papers is about 60, depending on the number of iterations
`until convergence. These values represent cluster links between the scored node and
`the contributing node. See the edge values (e.g. “.2”) from Figure 3 on page 5 of The
`PageRank Citation Ranking: Bringing Order to the Web (reproduced below).
`
`
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`As described in the formula above, PageRank is a recursive algorithm that analyzes
`portions of the set of direct links for contributions of web pages that are only
`indirectly related to the selected web page. Thus, the algorithm locates indirectly
`related nodes and scores relationships defined by paths of direct links between
`webpages that are indirectly related to each other. As seen in the figure below, the
`PageRank of the web page represented by node A (also referred to as PR(A)) is
`determined by the PageRank of web links that are back linked to A.
`
`Indirect Relationship
`
`
`
`Node A’s PageRank score reflects the scores of the PageRank of Node T1 (PR(T1))
`which is a function of the nodes that back link to it (Node 2), while the PageRank of
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`Node 2 is a function of the nodes that back link to it (not shown), and so on and so
`forth. As shown in the arc above, Node A’s PageRank is a function of Node 2’s
`PageRank, which is indirectly related to Node A. Node 2’s score is accounted for by
`the algorithm because it is indirectly related to Node A. The PageRank algorithm
`recursively propagates to link lengths up to approximately 50-60 iterations.
`
`The above described process is conducted in a series of iterative and recursive steps in
`which the cluster link set is analyzed during each iteration. Each iteration of the
`PageRank algorithm analyzes at least one additional link length of link relationships.
`For example, the second iteration may measure all cluster link relationships that are
`two link lengths from the scored node. Thus, during the second iteration, the ranking
`function (e.g., PageRank(A) will identify and add the weight of link relationships two
`link lengths away from the scored node in a manner similar to:
`
`Rank(A) = (1-d) [1+d(contribution of pages of paths of length 1) +
`d2(contribution of pages of paths of length 2)]
`
`The nodes that are identified during the first iteration are of a path length of 1 and are
`directly related to the chosen node. As described below, these nodes are then used to
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`locate indirectly related nodes to determine the contribution from those nodes.
`
`The third iteration would then measure link relationships that are three links lengths
`from the scoring node in a manner similar to:
`
`Rank(A) = (1-d) [1+d(contribution of pages of paths of length 1) +
`d2(contribution of pages of paths of length 2) + d3 (contribution of pages of
`paths of length 3)]
`
`The fourth iteration would measure link relationships that are four links lengths from
`the scoring node in a manner similar to:
`
`Rank(A) = (1-d) [1+d(contribution of pages of paths of length 1) +
`d2(contribution
`
`And so on with each iteration identifying and weighting an additional set of cluster
`link relationships of a given link length.
`
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`
`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`The above algorithm shows that the URLs are cluster analyzed for indirect
`relationships. Since the PageRank score of each selected web page reflects the scores
`of web pages directly linked to it and the PageRank scores of those web pages reflects
`the scores of web pages directly linked to them, the PageRank score of each selected
`web page is the result of a cluster analysis of indirect relationships and reflects the
`scores of web pages only indirectly related to the selected web page.
`
`displaying identities of web
`pages, wherein the located
`Universal Resource Locators
`are used to identify web pages.
`
`Search results including web pages identified by Universal Resource Locators are
`displayed to the user. The user may click on a link and request Google to display the
`full contents of the web page. Google provides an interface for receiving the inputs,
`processes the inputs, and sends appropriate instructions. Google also automatically
`displays a portion of the web page and in some cases the full contents of the web page.
`
`15
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`
`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`Google Search for “Google PageRank”
`
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`
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`
`
`21. A method of displaying
`information about a network
`that has hyperjump data,
`comprising:
`
`Google’s search engine that uses PageRank employs methods for visually
`displaying data relating to the World Wide Web (and other networks) that have
`hyperjump data:
`
`Google’s search engine that uses PageRank employs methods for visually displaying
`information related to the World Wide Web. Search results including identifiable web
`pages and URLs with pointers (a form of hyperjump data) are displayed to the user.
`The user may click on a URL provided by Google and request Google to display the
`full text of the web page. Google provides an interface for receiving the inputs,
`processes the inputs, and sends appropriate instructions. Google also automatically
`displays a portion of the web page and in some cases the full text of the web page.
`
`18
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`
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`
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`EXHIBIT 2052
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`Challenged Claims of ’571
`Patent
`
`Evidence of Infringement – Google’s Search Engine that uses PageRank
`
`Google Search for “Google PageRank”
`
`
`
`choosing a node;
`
`The PageRank algorithm chooses an identifiable node in order to analyze the link
`structure of the web and calculate a unique PageRank score for the individual node,
`
`19
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`Challenged Claims of ’571
`Patent
`
`Evidence of Infringement – Google’s Search Engine that uses PageRank
`
`which determines which nodes are displayed. In doing so, Google selects each node
`and conducts an analysis through mathematical calculation of the link structure of the
`web in relation to that specific selected node to determine a numerical score
`specifically associated with the node.
`
`This is clearly seen in one of the disclosed mathematically equivalent formulations of
`PageRank, where node A is selected and the analysis is subsequently computed with
`respect to the selected node A:
`
` “
`
` [T]he rank of a page A is defined according to the present invention as
`
`
`where Bl, ... , Bn are the backlink pages of A, r(Bl), ... , r(Bn ) are their ranks, |B1|, ... ,
`|Bn| are their numbers of forward links, and α is a constant in the interval [0,1], and N
`is the total number of pages in the web. Ex. 2086:’999 Patent, 4:15-25.
`
`Furthermore, hyperjump data associated with these nodes are captured and internally
`stored by Google, both literally and via a related unique number assigned to it
`internally by Google:
`
`20
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`EXHIBIT 2052
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`Challenged Claims of ’571
`Patent
`
`Evidence of Infringement – Google’s Search Engine that uses PageRank
`
`
`
`“We convert each URL into a unique integer, and store each hyperlink in a
`database using the integer IDs to identify pages.” Ex. 2054: The PageRank
`Citation Ranking: Bringing Order to the Web at 3.1
`
`
`Nodes (documents, webpages, hosts, sites, domains, blogs etc.) existing as or relating
`to webpages residing on the Web (or nodes in a related database) may have direct
`references from one node to another and indirect relationships though a series of
`connected hyperlinks. As part of its clustering analysis and the calculation of its ranks,
`Google’s Software also chooses contributing nodes to analyze for purposes of
`quantifying relationships between the scored nodes and the contributing nodes. An
`analysis unique to the contributing node in relation to the scored node is conducted.
`
`accessing the hyperjump data;
`
`PageRank accesses hyperjump data in order to perform link analysis on the chosen
`node. When a node is chosen for analysis, the link structure connecting the
`identified node to other nodes is determined and used to create an adapted
`adjacency matrix for use in the calculation of the PageRank algorithm. These
`matrices map the direct links between each node on the Web identified by Google.
`Ex. 2099: Langville, Amy and Meyer, Carl D, Google's PageRank and Beyond:
`
`21
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`EXHIBIT 2052
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`Challenged Claims of ’571
`Patent
`
`Evidence of Infringement – Google’s Search Engine that uses PageRank
`
`The Science of Search Engine Rankings, at 31-52 (Princeton University Press
`2006).
`
`The citation (link) graph of the web is an important resource that has largely
`gone unused in existing web search engines. We have created maps containing
`as many as 518 million of these hyperlinks, a significant sample of the total.
`Ex. 2053: The Anatomy of a Large-Scale Hypertextual Web Search Engine, at
`2.1.
`
`Google’s algorithm accesses the hyperjump data pursuant to the use of its
`PageRank algorithm to calculate the PageRank Scores
`
`The indexer performs another important function. It parses out all the links in
`every web page and stores important information about them in an anchors file.
`This file contains enough information to determine where each link points
`from and to, and the text of the link. … The URLresolver reads the anchors
`file … It also generates a database of links which are pairs of docIDs. The links
`database is used to compute PageRanks for all the documents.
`Ex. 2053: The Anatomy of a Large-Scale Hypertextual Web Search Engine, at
`
`22
`
`
`
`
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`EXHIBIT 2052
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`Challenged Claims of ’571
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`
`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`§4.1 (emphasis added)
`
`See also id. at 4.1 fig.1 (red box added) below:
`
`23
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`24
`Google identifies URLs by converting the URL string into a docID code:
`
`Additionally, there is a file which is used to convert URLs into docIDs. It is a
`
`
`
`
`
`
`
`
`
`Challenged Claims of ’571
`Patent
`
`identifying hyperjump data
`from within the accessed
`hyperjump data that has a direct
`reference to the chosen node;
`
`EXHIBIT 2052
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
`
`The calculation of PageRank identifies direct references to the chosen node (e.g.,
`forward links), from the accessed hyperjump data.
`
`
`The indexer performs another important function. It parses out all the links in
`every web page and stores important information about them in an anchors file.
`This file contains enough information to determine where each link points
`from and to, and the text of the link. … The URLresolver reads the anchors
`file … It also generates a database of links which are pairs of docIDs. The links
`database is used to compute PageRanks for all the documents.
`The Anatomy of a Large-Scale Hypertextual Web Search Engine, at §4.1
`(emphasis added)
`
`See also id. at 4.1 fig.1 (red box added) below:
`
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`26
`Google identifies URLs by converting the URL string into a docID code:
`
`Additionally, there is a file which is used to convert URLs into docIDs. It is a
`
`
`
`
`
`
`
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`Challenged Claims of ’571
`Patent
`
`determining hyperjump data
`from within the accessed
`hyperjump data that has an
`indirect reference to the chosen
`node using the identified
`hyperjump data, wherein the
`step of determining comprises
`cluster analyzing the hyperjump
`data; and
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`EXHIBIT 2052
`
`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`PageRank analyzes the accessed hyperjump data to determine indirect relationships
`with the chosen node, and cluster analyzes the hyperjump data for indirect
`relationships. The cluster analysis includes non-semantically generating a set of
`candidate cluster links for nodes indirectly related to the chosen node using the
`hyperjump data, assigning weights to the candidate cluster links and deriving actual
`cluster links from the set of candidate cluster links based on the assigned weights.
`
`PageRank analyzes hyperjump data
`
`Google obtains and stores information concerning the hyperlink structure of the web
`based on the chosen nodes and identified Universal Resource Locators in a link
`database. Google’s Software includes methods of analyzing URLs stored in the
`database of links to build representations of direct relationships between nodes (e.g.,
`web page, domain, site, blog, or website). For example, the links database is used to
`create an adapted adjacency matrix for use in the calculation of the PageRank
`algorithm. This algorithm (described in further detail below) analyzes the identified
`URLs by building representations based on the link structure of the identified URLs
`and by calculating the PageRanks of all the documents based on the links database
`which contains information regarding the identified URLs. See limitation directly
`above. These matrices map the direct links between each node on the Web. Langville,
`27
`
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`
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`EXHIBIT 2052
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`Challenged Claims of ’571
`Patent
`
`Evidence of Infringement – Google’s Search Engine that uses PageRank
`
`Ex. 2099: Langville, Amy and Meyer, Carl D, Google's PageRank and Beyond: The
`Science of Search Engine Rankings, at 31-52 (Princeton University Press 2006).
`
`PageRank determines indirect relationship with the chosen node using the
`accessed hyperjump data.
`
`Google’s PageRank algorithm is a recursive mathematical algorithm that analyze
`portions of the set of direct links for contributions of websites, nodes, and other
`objects that are indirectly linked to the objects being scored. The formula for
`calculating the PageRank of the page, as provided by the paper The Anatomy of a
`Large Scale Search Engine, by Brin and Page (1998) is as follows:
`
`We assume page A has pages T1....Tn which point to it (i.e., are citations). The
`parameter d is a damping factor which can be set between 0 and 1. We usually set d to
`0.85. Also C(A) is defined as the number of links going out of page A. The PageRank
`of a page A is given as follows:
`
`PR(A) = (1-d) + d(PR(T1)/C(T1) + .... + PR(Tn)/C(Tn))
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`Challenged Claims of ’571
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`The above algorithm, including Google’s subsequent elaborations on the basic
`formula, is applied recursively and measures contributions from indirectly related
`nodes. See Ex. 2099: Langville, Amy and Meyer, Carl D, Google’s PageRank and
`Beyond: The Science of Search Engine Rankings, at 31-52 (Princeton University Press
`2006).
`
`The above recursive algorithm shows links indirectly related to a node nevertheless
`directly contribute to the PageRank score of that node. By recursively analyzing link
`relationships that are only indirectly related to the selected object, Google’s algorithm
`necessarily locates, identifies, and analyzes URLs which have only an indirect
`relationship with the chosen node.
`
`PageRank non-semantically generates a set of candidate cluster links for nodes
`indirectly related to the chosen node
`
`The calculation of PageRank is non-semantic. Ex. 2054: The PageRank Citation
`Ranking: Bringing Order to the Web at 15 (“PageRank is a global ranking of all web
`pages, regardless of their content, based solely on their location in the Web's graph
`structure.”).
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`Challenged Claims of ’571
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`An example of cluster analyzing is described in step 3012 of Fig. 14B of the ’571
`patent.
`
`The PageRank algorithm analyzes clusters of links (i.e., multiple relationships) within
`a specific path length from a selected node to generate a PageRank score for the
`selected node. During each iteration, the algorithm calculates the amount of
`contribution to the PageRank score by nodes of a specific path length. The maximum
`path length described in its papers is about 60, depending on the number of iterations
`until convergence. These values represent cluster links between the scored node and
`the contributing node. See the edge values (e.g. “.2”) from Figure 3 on page 5 of Ex.
`2054: The PageRank Citation Ranking: Bringing Order to the Web (reproduced
`below).
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`Challenged Claims of ’571
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`
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`As described in the formula above, PageRank is a recursive algorithm that analyzes
`portions of the set of direct links for contributions of nodes that are only indirectly
`related to the selected node. Thus, the algorithm locates indirectly related nodes and
`scores relationships defined by paths of direct links between nodes that are indirectly
`related to each other. As seen in the figure below, the PageRank of the node
`represented by node A (also referred to as PR(A)) is determined by the PageRank of
`direct references that are back linked to A.
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`Indirect Relationship
`
`
`
`Node A’s PageRank score reflects the scores of the PageRank of Node T1 (PR(T1))
`which is a function of the nodes that back link to it (Node 2), while the PageRank of
`Node 2 is a function of the nodes that back link to it (not shown), and so on and so
`forth. As shown in the arc above, Node A’s PageRank is a function of Node 2’s
`PageRank, which is indirectly related to Node A. Node 2’s score is accounted for by
`the algorithm because it is indirectly related to Node A. The PageRank algorithm
`recursively propagates to link lengths up to approximately 50-60 iterations. See, e.g.,
`Ex. 2054: The PageRank Citation Ranking: Bringing Order to the Web at 7 (“As can
`be seen from the graph in Figure 4 PageRank on a large 322 million link database
`converges to a reasonable tolerance in roughly 52 iterations.”). This set of cluster
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`links of a limited link length constitutes one potential set of candidates cluster
`links.
`
`The above described process is conducted in a series of iterative and recursive steps in
`which the cluster link set is analyzed during each iteration. Each iteration of the
`PageRank algorithm analyzes at least one additional link length of link relationships.
`For example, the second iteration may measure all cluster link relationships that are
`two link lengths from the scored node. Thus, during the second iteration, the ranking
`function (e.g., PageRank(A) will identify and add the weight of link relationships two
`link lengths away from the scored node in a manner similar to:
`
`Rank(A) = (1-d) [1+d(contribution of nodes of paths of length 1) +
`d2(contribution of nodes of paths of length 2)]
`
`The nodes that are identified during the first iteration are of a path length of 1 and are
`directly related to the chosen node. As described below, these nodes are then used to
`locate indirectly related nodes to determine the contribution from those nodes.
`
`The third iteration would then measure link relationships that are three links lengths
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`from the scoring node in a manner similar to:
`
`Rank(A) = (1-d) [1+d(contribution of nodes of paths of length 1) +
`d2(contribution of nodes of paths of length 2) + d3 (contribution of nodes of
`paths of length 3)]
`
`The fourth iteration would measure link relationships that are four links lengths from
`the scoring node in a manner similar to:
`
`Rank(A) = (1-d) [1+d(contribution of nodes of paths of length 1) +
`d2(contribution of nodes of paths of length 3) + d4 (contribution of nodes of
`paths of length 4)]
`
`And so on with each iteration identifying and weighting an additional set of cluster
`link relationships of a given link length. Thus, each candidate cluster link is
`assigned a weight.
`
`The above algorithm shows that the nodes are cluster analyzed for indirect
`relationships. Since the PageRank score of each selected node reflects the scores of
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`Challenged Claims of ’571
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`Evidence of Infringement – Google’s Search Engine that uses PageRank
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`nodes directly linked to it and the PageRank scores of those nodes reflects the scores
`of nodes directly linked to them, the PageRank score of each selected node is the
`result of a cluster analysis of indirect
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