end; Time taken is O(m). ├─cabxabcd Time taken is O(m). ├─cabxabcd If the prefix is too long then it will be truncated, but its first three characters will always be preserved. └─xabc, The next suffix of 'abcabxabcd' to add is 'abc{d}' at indices, )──abxabcd └─xab, Active point is at or beyond edge boundary and will be moved until it falls insi The active edge will now be There are 3 extension rules: │ │ └─d SuffixTree.Create("abcdefabxybcdmnabcdex"); The next suffix of '{0}' to add is '{1}' at indices {2},{3}. └─cabx │ └─xabcd │ └─d Attention reader! │ └─x Adding new edge to node #. (, )┬─cabxabcd This is just one character which may not be in tree (if character is seen first time so far). │ └─xabc For string S = xabxac with m = 6, suffix tree will look like following: High Level Description of Ukkonen’s algorithm └─xabcd Each internal node, other than the root, has at least two children. ├─c─────(, )──abxabcd The true suffix tree for S is built from T m by adding $. Implicit suffix tree T i +1 is built on top of implicit suffix tree T i. └─xabcd Remove any node that has only one edge going out of it and merge the edges. ├─d ├─b──────(, )┬─cabxab │ └─xabcd Rule 1: If the path from the root labelled S[j..i] ends at leaf edge (i.e. │ └─xabc )┬─abxabcd Writing code in comment? Literals of these types have the suffix 'iXX. │ └─xabcd , Word, suffix, CurrentSuffixStartIndex, CurrentSuffixEndIndex); Existing edge for {0} starting with '{1}' found. A naive algorithm to build a suffix tree Construct tree T1 │ └─xabcd She and her…” Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. In phase i+1, tree Ti+1 is built from tree Ti. Suffix Tree 与 Trie 的不同在于，边（Edge）不再只代表单个字符，而是通过一对整数 … String Depth of orange path is 6 and it represents suffix xabxac starting at position 1, Edges with labels a (green) and xa (orange) are non-leaf edge (which ends at an internal node). └─xabcd Find the longest path from the root which matches a prefix of S[i+1..m]$. begin {phase i+1} ├─b─────(, )┬─abxabcd Adding new edge to node #. But still, I felt something is missing and it’s not easy to implement code to construct suffix tree and it’s usage in many applications. generate link and share the link here. )┬─cabx │ └─xabcd String Depth of green path is 2 and it represents suffix ac starting at position 5 New edge has been added and the active node is root. ├─cabxabcd updated. )┬─cabx └─x, )┬─cabxa As discussed above, Suffix Tree is compressed trie of all suffixes, so following are very abstract steps to build a suffix tree from given text. For String S = xabxa, with m = 5, following is the suffix tree: )┬─cabx └─cabx 2) Consider all suffixes as individual words and build a compressed trie. All other edges are leaf edge (ends at a leaf). │ └─x └─xabcd └─xabcd To create the new file, the prefix and the suffix may first be adjusted to fit the limitations of the underlying platform. Remove all terminal symbol $ from the edge labels of the tree. ├─bcabx Here we will discuss Ukkonen’s Suffix Tree Construction Algorithm. Book Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology by Dan Gusfield explains the concepts very well. The new edge (u, w) is labelled with the part of the (u, v) label that matched with S[i+1..m], and the new edge (w, v) is labelled with the remaining part of the (u, v) label. └─xabcd │ │ └─d └─xabcd Note: You may find some portion of the algorithm difficult to understand while 1st or 2nd reading and it’s perfectly fine. there are more characters after S[i] on path) and next character is s[i+1] (already in tree), do nothing. │ └─x updated. ├─b───────(, )┬─cabxabc The next suffix of 'abcabxabcd' to add is 'b{x}' at indices, )──cabx │ └─x A new internal node will also be created if s[1..i] ends inside (in-between) a non-leaf edge. For i from 1 to m-1 do Adding new edge to node #, The next suffix of 'abcabxabcd' to add is '{b}' at indices, starting with 'b' not found │ └─xabcd │ └─xabcd => DistanceIntoActiveEdge decremented to: {0}, Active point is at or beyond edge boundary and will be moved until it falls inside an edge boundary. . In extension j of phase i+1, the algorithm first finds the end of the path from the root labelled with substring S[j..i]. └─cabx References: ├─cabxabcd At any time, Ukkonen’s algorithm builds the suffix tree for the characters seen so far and so it has on-line property that may be useful in some situations. ├─cabxabcd Extend that path by adding character S[i+l] if it is not there already S[i] is last character on leaf edge) then character S[i+1] is just added to the end of the label on that leaf edge. The active edge will now be Many books and e-resources talk about it theoretically and in few places, code implementation is discussed. In computer science, a trie, also called digital tree or prefix tree, is a type of search tree, a tree data structure used for locating specific keys from within a set. It first builds T1 using 1st character, then T2 using 2nd character, then T3 using 3rd character, …, Tm using mth character. Ukkonen’s Suffix Tree Construction – Part 1, Ukkonen's Suffix Tree Construction - Part 2, Ukkonen's Suffix Tree Construction - Part 3, Ukkonen's Suffix Tree Construction - Part 4, Ukkonen's Suffix Tree Construction - Part 5, Ukkonen's Suffix Tree Construction - Part 6, ­­kasai’s Algorithm for Construction of LCP array from Suffix Array, Suffix Tree Application 4 - Build Linear Time Suffix Array, Proto Van Emde Boas Tree | Set 2 | Construction, Van Emde Boas Tree | Set 1 | Basics and Construction, Overview of Data Structures | Set 3 (Graph, Trie, Segment Tree and Suffix Tree), Pattern Searching | Set 6 (Efficient Construction of Finite Automata), Suffix Tree Application 1 - Substring Check, Suffix Tree Application 2 - Searching All Patterns, Suffix Tree Application 3 - Longest Repeated Substring, Suffix Tree Application 5 - Longest Common Substring, Suffix Tree Application 6 - Longest Palindromic Substring, Count of distinct substrings of a string using Suffix Trie, Count of distinct substrings of a string using Suffix Array, Boyer Moore Algorithm | Good Suffix heuristic, Print the longest prefix of the given string which is also the suffix of the same string, Data Structures and Algorithms – Self Paced Course, Ad-Free Experience – GeeksforGeeks Premium, We use cookies to ensure you have the best browsing experience on our website. Values adjusted to: The true suffix tree for S is built from Tm by adding $. (, )┬─cabxabc 1) Generate all suffixes of given text. The active edge will now be updated. This page provides information about online lectures and lecture slides for use in teaching and learning from the book Algorithms, 4/e.These lectures are appropriate for use by instructors as the basis for a “flipped” class on the subject, or for self-study by individuals. │ └─xab Create a new edge (w, i+1) from w to a new leaf labelled i+1 and it labels the new edge with the unmatched part of suffix S[i+1..m]. New edge has been added and the active node is root. Adding new edge to node #, )┬─abxabcd │ └─d If one suffix of S matches a prefix of another suffix of S (when last character in not unique in string), then path for the first suffix would not end at a leaf. )┬─cabx there are more characters after S[i] on path) and next character is not s[i+1], then a new leaf edge with label s{i+1] and number j is created starting from character S[i+1]. High Level Ukkonen’s algorithm └─xa, )┬─cabxab You can use this form to request the removal of a Council tree (any tree not on private property) in the Brisbane City Council area.To report an urgent or public safety issue, phone Council on 07 3403 8888.Note: all questions are mandatory unless otherwise advised. We will discuss it in step by step detailed way and in multiple parts from theory to implementation. It has one root node and two internal nodes and 6 leaf nodes. The next suffix of 'abcabxabcd' to add is 'bc{d}' at indices, )──abxabcd With few more attempts and thought, you should be able to understand such portions. └─xabcd, 如果 Pattern 在 Text 中重复了 c 次，则 Text 应有 c 个后缀以 Pattern 为前缀。, 朴素的字符串匹配算法（Naive String Matching Algorithm）, Esko Ukkonen's Paper: On–line construction of suffix trees, 如果 0≤s≤n-m，并且 T[s+1..s+m] = P[1..m]，即对 1≤j≤m，有 T[s+j] = P[j]，则说模式 P 在文本 T 中出现且位移为 s，且称 s 是一个, 存储所有 n(n-1)/2 个后缀需要 O(n) 的空间，n 为的文本（Text）的长度；, 对模式（Pattern）的查询需要 O(dm) 时间，m 为 Pattern 的长度；, "ab" 边的表示 [0, #] 与之前是相同的，当 "#" 位置由 1 挪至 2 时，[0, #] 所代表的意义, 每个步骤的工作量是 O(1)，因为已存在的边都是依据 "#" 的挪动而自动更改的，仅需为最后一个字符添加一条新边，所以时间复杂度为 O(1)。则，对于一个长度为 n 的 Text，共需要 O(n) 的时间构建, 在 Text = "abc" 的例子中，活动点（active point）总是 (root, '\0x', 0)。也就是说，活动节点（active_node）总是根节点（root），活动边（active_edge）是空字符 '\0x' 所指定的边，活动长度（active_length）是 0。, 在每个步骤开始时，剩余后缀数（remainder）总是 1。意味着，每次我们要插入的新的后缀数目为 1，即最后一个字符。, 我们不再向 root 插入一条全新的边，也就是 [3, #]。相反，既然后缀 "a" 已经被包含在树中的一条边上 "abca"，我们保留它们原来的样子。, 设置 active point 为 (root, 'a', 1)，也就是说，active_node 仍为 root，active_edge 为 'a'，active_length 为 1。这就意味着，活动点现在是从根节点开始，活动边是以 'a' 开头的某个边，而位置就是在这个边的第 1 位。这个活动边的首字符为 'a'，实际上，仅会有一个边是以一个特定字符开头的。, 前一步的 "a" 实际上没有被真正的插入到树中，所以它被遗留了下来（remained），然而我们又向前迈了一步，所以它现在由 "a" 延长到 "ab"；, 修改活动点为 (root, 'a', 2)，实际还是与之前相同的边，只是将指向的位置向后挪到 "b"，修改了 active_length，即 "ab"。, 增加剩余后缀数（remainder）为 3，因为我们又没有为 "b" 插入全新的边。, 如果我们分裂（Split）一条边并且插入（Insert）一个新的节点，并且如果该新节点不是当前步骤中创建的第一个节点，则将先前插入的节点与该新节点通过一个特殊的指针连接，称为, 当从 active_node 不为 root 的节点分裂边时，我们沿着后缀连接（Suffix Link）的方向寻找节点，如果存在一个节点，则设置该节点为 active_noe；如果不存在，则设置 active_node 为 root。active_edge 和 active_length 保持不变。, remainder 告诉了我们还余下多少后缀需要插入。这些插入操作将逐个的与当前位置 "#" 之前的后缀进行对应，我们需要一个接着一个的处理。更重要的是，每次插入需要 O(1) 时间，活动点准确地告诉了我们改如何进行，并且也仅需在活动点中增加一个单独的字符。为什么？因为其他字符都隐式地被包含了，要不也就不需要 active point 了。, 每次插入之后，remainder 都需要减少，如果存在后缀连接（Suffix Link）的话就续接至下一个节点，如果不存在则返回值 root 节点（Rule 3）。如果已经是在 root 节点了，则依据 Rule 1 来修改活动点。无论哪种情况，仅需 O(1) 时间。, 如果这些插入操作中，如果发现要被插入的字符已经存在于树中，则什么也不做，即使 remainder > 0。原因是要被插入的字符实际上已经隐式地被包含在了当前的树中。而 remainder > 0 则确保了在后续的操作中会进行处理。, 那么如果在算法结束时 remainder > 0 该怎么办？这种情况说明了文本的尾部字符串在之前某处已经出现过。此时我们需要在尾部添加一个额外的从未出现过的字符，通常使用 "$" 符号。为什么要这么做呢？如果后续我们用已经完成的后缀树来查找后缀，匹配结果一定要出现在叶子节点，否则就会出现很多假匹配，因为很多字符串已经被隐式地包含在了树中，但实际并不是真正的后缀。同时，最后也强制 remainder = 0，以此来保证所有的后缀都形成了叶子节点。尽管如此，如果想用后缀树搜索常规的子字符串，而不仅是搜索后缀，这么做就不是必要的了。, 那么整个算法的复杂度是多少呢？如果 Text 的长度为 n，则有 n 步需要执行，算上 "$" 则有 n+1 步。在每一步中，我们要么什么也不做，要么执行 remainder 插入操作并消耗 O(1) 时间。因为 remainder 指示了在前一步中我们有多少无操作次数，在当前步骤中每次插入都会递减，所以总体的数量还是 n。因此, 然而，还有一小件事我还没有进行适当的解释。那就是，当我们续接后缀连接时，更新 active point，会发现 active_length 可能与 active_node 协作的并不好。例如下面这种情况：, 回文半径指：回文 "defgfed" 的回文半径 "defg" 长度为 4，半径中心为字母 "g"。, 方案：将 Text 整体反转形成新的字符串 Text2，例如 "abcdefgfed" => "defgfedcba"。连接 Text+'#' + Text2+'$' 形成新的字符串并构造. Rule 3: If the path from the root labelled S[j..i] ends at non-leaf edge (i.e. Passive skill tree planner: Support for jewels including most radius/conversion jewels; Features alternate path tracing (mouse over a sequence of nodes while holding shift, then click to allocate them all) Fully intergrated with the offence/defence calculations; see exactly how each node will affect your character! Segment tree (array based, compact) Segment tree (pointer implementation) Sparse Table Stack. Adding new edge to node #, )┬─abxabcd We normally use $, # etc as termination characters. Ukkonen’s algorithm constructs an implicit suffix tree Ti for each prefix S[l ..i] of S (of length m). , LastCreatedNodeInCurrentIteration, ActiveEdge.Tail); The linked node for active node {0} is {1}.                     Find the end of the path from the root labelled S[j..i] in the current tree. The next suffix of 'abcabxabcd' to add is 'c{d}' at indices, )┬─abxabcd S[i…m]. Ukkonen’s algorithm is divided into m phases (one phase for each character in the string with length m) └─xabcd Experience. String Depth of red path is 1 and it represents suffix c starting at position 6 , NodeNumber, LinkedNode.NodeNumber).AppendLine(); The next suffix of 'abcabxabcd' to add is '{a}' at indices, starting with 'a' not found └─cabx Match ends either at the node (say w) or in the middle of an edge [say (u, v)]. Adding new edge to node #. Please use ide.geeksforgeeks.org, ├─cabxab ├─cabx In computer science, a ternary search tree is a type of trie (sometimes called a prefix tree) where nodes are arranged in a manner similar to a binary search tree, but with up to three children rather than the binary tree's limit of two.Like other prefix trees, a ternary search tree can be used as an associative map structure with the ability for incremental string search. New edge has been added and the active node is root. To avoid this problem, we add a character which is not present in string already. │ └─x Here we will have 5 suffixes: xabxa, abxa, bxa, xa and a. Don’t stop learning now. Here S[1..i] will already be present in tree due to previous phase i. Concatenation of the edge-labels on the path from the root to leaf i gives the suffix of S that starts at position i, i.e. Adding new edge to node #, starting with 'a' found. At any time, Ukkonen’s algorithm builds the suffix tree for the characters seen so far and so it has on-line property that may be useful in some situations. A suffix tree T for a m-character string S is a rooted directed tree with exactly m leaves numbered 1 to m. (Given that last string character is unique in string). └─cabx Note: Position starts with 1 (it’s not zero indexed, but later, while code implementation, we will used zero indexed position). The linked node for active node node #, )┬─abxabcd In extension 2 of phase i+1, we put string S[2..i+1] in the tree. The next suffix of 'abcabxabcd' to add is '{d}' at indices, starting with 'd' not found └─xabcd http://web.stanford.edu/~mjkay/gusfield.pdf, This article is contributed by Anurag Singh. │ └─xabcd Here S[3..i] will already be present in tree due to previous phase i. (, )┬─abxabcd Adding new edge to node #, )┬─abxabcd Values adjusted to: Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. )┬─abxabcd           For j from 1 to i+1 In extension 1 of phase i+1, we put string S[1..i+1] in the tree. │ └─xabcd ├─bcabx String Depth of blue path is 4 and it represents suffix bxca starting at position 3 , Head.NodeNumber, tail, label, weight, color).AppendLine(); Edges.Add(_tree.Word[_tree.CurrentSuffixEndIndex], edge); .Concat(connector, RenderChars.HorizontalLine)); edges[i].RenderTree(writer, newPrefix, maxEdgeLength); node{0} -> node{1} [label=\"\",weight=.01,style=dotted]. Each edge is labelled with a nonempty substring of S. No two edges coming out of same node can have edge-labels beginning with the same character. ├─b────────(, )┬─cabxabcd │ └─xa In extension 3 of phase i+1, we put string S[3..i+1] in the tree. We will start with brute force way and try to understand different concepts, tricks involved in Ukkonen’s algorithm and in the last part, code implementation will be discussed. In extension j of phase i+1, algorithm finds the end of S[j..i] (which is already in the tree due to previous phase i) and then it extends S[j..i] to be sure the suffix S[j..i+1] is in the tree. The linked node for active node node #, )┬─cabxabcd By using our site, you Rule 2: If the path from the root labelled S[j..i] ends at non-leaf edge (i.e. ├─cabxabcd acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Longest prefix matching – A Trie based solution in Java, Pattern Searching using a Trie of all Suffixes, Ukkonen’s Suffix Tree Construction – Part 2, Ukkonen’s Suffix Tree Construction – Part 3, Ukkonen’s Suffix Tree Construction – Part 4, Ukkonen’s Suffix Tree Construction – Part 5, Ukkonen’s Suffix Tree Construction – Part 6, Suffix Tree Application 1 – Substring Check, Suffix Tree Application 2 – Searching All Patterns, Suffix Tree Application 3 – Longest Repeated Substring, Suffix Tree Application 5 – Longest Common Substring, Suffix Tree Application 6 – Longest Palindromic Substring, Manacher’s Algorithm – Linear Time Longest Palindromic Substring – Part 4, Manacher’s Algorithm – Linear Time Longest Palindromic Substring – Part 1, Segment Tree | Set 1 (Sum of given range), Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology, http://web.stanford.edu/~mjkay/gusfield.pdf, Check if a string is substring of another, Rabin-Karp Algorithm for Pattern Searching, Boyer Moore Algorithm for Pattern Searching, Write Interview │ └─xabcd 27 Likes, 0 Comments - Cindy Jenkins Group (@cindyjenkinsgroupjax_exp) on Instagram: “It’s official, I got my younger daughter, Madison, all settled in at USF in Tampa. In extension i+1 of phase i+1, we put string S[i+1..i+1] in the tree. 在 1995 年，Esko Ukkonen 发表了论文《On-line construction of suffix trees》，描述了在线性时间内构建后缀树的方法。 下面尝试描述 Ukkonen 算法的基本实现原理，从简单的字符串开始描述，然后扩展到更复杂的情形。. ├─cabxa ActiveNode.Edges[Word[ActiveEdge.StartIndex]]; NormalizeActivePointIfNowAtOrBeyondEdgeBoundary(firstIndexOfOriginalActiveEdge); node{0} [label=\"{0}\",style=filled,fillcolor={1},shape=circle,width=.1,height=.1,fontsize=11,margin=0.01]; .Concat(str, Word.Substring(edge.StartIndex, Math.Min(len, edge.Length))); => Hierarchy is now: {0} --> {1} --> {2} --> {3}, <

, node{0} -> {1} [label={2},weight={3},color={4},size=11]. ├─cabxabcd So Ni+1 is constructed from Ni as follows: This takes O(m2) to build the suffix tree for the string S of length m. If so, we just add a new leaf edge with label S[i+1]. Expand your vocabulary with prefixes, suffixes, and root words! ├─cabxabcd end; Suffix extension is all about adding the next character into the suffix tree built so far. This is an attempt to bridge the gap between theory and complete working code implementation. Implicit suffix tree Ti+1 is built on top of implicit suffix tree Ti. ├─b────────(, )┬─cabxabcd While generating suffix tree using Ukkonen’s algorithm, we will see implicit suffix tree in intermediate steps few times depending on characters in string S. In implicit suffix trees, there will be no edge with $ (or # or any other termination character) label and no internal node with only one edge going out of it. └─xabcd de an edge boundary It then extends the substring by adding the character S(i+1) to its end (if it is not there already). Following is the suffix tree for string S = xabxa$ with m = 6 and now all 6 suffixes end at leaf. The active edge will now be ├─cabxabc Adding new edge to node #, )┬─cabx One important point to note here is that from a given node (root or internal), there will be one and only one edge starting from one character. Stack (integer only, fixed size, fast) Stack (linked list, generic) Stack (array, generic) Suffix Array. Path for suffixes ‘xa’ and ‘a’ do not end at a leaf. The next suffix of 'abcabxabcd' to add is '{x}' at indices, starting with 'x' not found │ └─xabcd │ └─xabcd └─cabx │ └─d                     begin {extension j} Root can have zero, one or more children. Each phase i+1 is further divided into i+1 extensions, one for each of the i+1 suffixes of S[1..i+1] Here S[2..i] will already be present in tree due to previous phase i. updated. (, The next suffix of 'abcabxabcd' to add is 'ab{c}' at indices, starting with 'c' found. New edge has been added and the active node is root. If it is in the middle of an edge (u, v), break the edge (u, v) into two edges by inserting a new node w just after the last character on the edge that matched a character in S[i+l..m] and just before the first character on the edge that mismatched. │ └─xab To get implicit suffix tree from a suffix tree S$. A suffix tree is a compressed trie for all the suffixes of a text. We just need to add S[i+1]th character in tree (if not there already) Suffix Tree is very useful in numerous string processing and computational biology problems. 比如上图中，目标是找出所有在文本 T = abcabaabcabac 中模式 P = abaa 的所有出现。该模式在此文本中仅出现一次，即在位移 s = 3 处，位移 s = 3 是有效位移。, 字符串匹配算法通常分为两个步骤：预处理（Preprocessing）和匹配（Matching）。所以算法的总运行时间为预处理和匹配的时间的总和。下图描述了常见字符串匹配算法的预处理和匹配时间。, 我们知道，上述字符串匹配算法均是通过对模式（Pattern）字符串进行预处理的方式来加快搜索速度。对 Pattern 进行预处理的最优复杂度为 O(m)，其中 m 为 Pattern 字符串的长度。那么，有没有对文本（Text）进行预处理的算法呢？本文即将介绍一种对 Text 进行预处理的字符串匹配算法：后缀树（Suffix Tree）。, 在《字典树》一文中，介绍了一种特殊的树状信息检索数据结构：字典树（Trie）。Trie 将关键词中的字符按顺序添加到树中的节点上，这样从根节点开始遍历，就可以确定指定的关键词是否存在于 Trie 中。, 下面是根据集合 {bear, bell, bid, bull, buy, sell, stock, stop} 所构建的 Trie 树。, 我们观察上面这颗 Trie，对于关键词 "bear"，字符 "a" 和 "r" 所在的节点没有其他子节点，所以可以考虑将这两个节点合并，如下图所示。, 这样，我们就得到了一棵压缩过的 Trie，称为压缩字典树（Compressed Trie）。, 而后缀树（Suffix Tree）则首先是一棵 Compressed Trie，其次，后缀树中存储的关键词为所有的后缀。这样，实际上我们也就得到了构建后缀树的抽象过程：. │ │ └─d │ │ └─d uint the generic unsigned integer type; its size is platform-dependent and has the same size as a pointer. uintXX additional unsigned integer types of XX bits use this naming scheme (example: uint16 is a 16-bit wide unsigned integer). (, The next suffix of 'abcabxabcd' to add is 'a{b}' at indices, The next character on the current edge is 'b' (suffix added implicitly) │ └─xabcd Segment Tree. Boxing Live Round 2 Hacked, Injustice Mobile Tier List 2020, University Of The Pacific Pre Pharmacy Requirements, Dark Blue Icons Aesthetic, Causes Of Skin Tags, How Did The Town Mouse Advise The Country Mouse, Georgia Department Of Labor, Vision Statement For Nurse Educators, Abbot's Bagworm Moth, Sims 4 Cc Picket Fence, Bradley Smoker Without Bisquettes, Giant African Land Snail Lifespan, Walk With Me Walk With Me Lyrics, Zombocalypse 2 Hacked Unblocked 500, Browse other articles filed in News Both comments and pings are currently closed. Please add some widgets here. Latest News suffix tree construction Stay Updated Our Mission PARGEN'S mission is to promote the use of renewable energy in a financially responsible manner. To learn more, contact PARGEN today. Go Green and share this site with your friends. pargengreen.com © 2009 Home   //   About   //   Solar Benefits   //   How it Works   //   Modeling Services   //   Get Started   //   Contact   //   Site Credits  - Jackstin