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<metadata xml:lang="en"><Esri><MetaID>{04E32566-55C3-4BEA-B45A-E67B19D4BAD8}</MetaID><CreaDate>20050721</CreaDate><CreaTime>12000200</CreaTime><SyncOnce>TRUE</SyncOnce><ModDate>20061128</ModDate><ModTime>094033</ModTime></Esri><tool name="FourColorMap" displayname="Four-Color a Map" toolboxalias=""><summary><para>Assigns a number from 1 to 4 to an integer column in a Featureclass. If a Unique Value renderer is made using the column, the map will be colored so that no two polygons that share a border will be given the same color. Polygons that do not have neighbors, for instance, Alaska and Hawaii on a map of the U.S., will not be assigned a number. They retain the number they initially had. Multi-part polygons or polygons in a region surrounding multi-part polygons may require more than 4 colors. Polygons that meet at a single point are not considered to be neighbors.</para></summary><parameters><param name="in_featureclass" displayname="Input Polygon Featureclass" type="Required" direction="Input" expression="<in_featureclass>"><commandReference><para>Polygon Featureclass to be assigned 4 colors.</para></commandReference><dialogReference><para>Polygon Featureclass to be assigned 4 colors. Can be the featureclass associated with a layer in the map, or a featureclass on disk. Warning! The tool uses a TopologyGraph. The time and memory usage necessary to build a TopologyGraph depend on the amount of vertices in the featureclass geometry, and is proportional to the log of the number of vertices times the number of vertices. At ArcGIS 9.1, building a TopologyGraph may begin using virtual memory (swapping) if the number of vertices being processed is large. The largest number of polygons that this tool has been tested on is around 16,000. A TopologyGraph can probably be built for a feature class with significantly more polygons if it has significantly fewer vertices. Simplifying the geometry is an option. The coloring algorithm runs in a time directly proportional to the number of polygons in the featureclass. The running time for this tool is most influenced by the time required to build the TopologyGraph not by the time required to color the map.</para></dialogReference></param><param name="in_field" displayname="Field getting Colors (1-4)" type="Required" direction="Input" expression="<in_field>"><commandReference><para>An integer field in the Featureclass that will be assigned the color.</para></commandReference><dialogReference><para>An integer field in the Featureclass that will be assigned the color, which is a number from 1 to 4.</para></dialogReference></param></parameters><toolIllust src="" alt=""></toolIllust><usage/><commandExample>FourColorMap US_States Colors</commandExample><scriptExample>FourColorMap(US_States, Colors)</scriptExample></tool><dataIdInfo><idCitation><resTitle>Four-Color a Map</resTitle><citRespParty><rpIndName>Tom Gross</rpIndName><rpOrgName>ESRI Benchmarks</rpOrgName><rpPosName></rpPosName><role><RoleCd>010</RoleCd></role><rpCntInfo><cntAddress><delPoint></delPoint><city></city><adminArea></adminArea><postCode></postCode><country></country><eMailAdd>[email protected]</eMailAdd></cntAddress><cntPhone><voiceNum></voiceNum><faxNum></faxNum></cntPhone></rpCntInfo></citRespParty></idCitation><idAbs>Implementation of a linear-time 4-color algorithm, which makes use of the 5-color algorithm as described in, "A Linear Algorithm for Colouring Planar Graphs with Five Colours" by M.H. Williams, The ComputerJournal, Vol 28, Number 1, (1985). The purpose is to assign a number between 1 and 4 to each polygon in a Featureclass so that no neighboring polygons are assigned the same number. The algorithm is implemented in a COM object called, Topo4Color, that can be run in-process in ArcMap, by a VBA client. It requires a TopologyGraph for input, and uses it to make the in-memory lists of adjacent polygons that the algorithm uses. The COM object is also wrapped in this Geoprocessor Function, FourColorMapFunction. The algorithm first uses the 5-Color algorithm to assign 5 colors. The 5-Color algorithm does this parsimoniously, meaning that it doesn't assign a higher number until necessary. For instance, the 5-Color part of the algorithm only uses 4 colors for a map of the United States. When there are polygons assigned color 5 after the 5-Color part of the algorithm finishes, a second phase tries to replace the color 5 with one of the other 4 colors by using a method called Kempe Chains. If there are still polygons with color 5 remaining, the algorithm switches the color 5 with a neighbor, and tries the Kempe Chain method again. This switching happens in a loop that also uses backtracking. If the loop fails to find a solution within a reasonable number of iterations it gives up and a color 5 will remain in the map. Since neither the 5-color algorithm nor any 4-color algorithm can be guaranteed to color a non-planar map, there is no provision for multiple polygons meeting at a point to be considered neighbors. If there are multipart polygons, the algorithm may fail to four-color the map. For instance, this happens when coloring the zip code polygons of Kentucky. Multipart polygons also make a non-planar map, but they often can be colored with 4 colors by this algorithm.</idAbs><descKeys KeyTypCd="005"><keyTyp><keyTyp>005</keyTyp></keyTyp><keyword>Map Coloring</keyword><keyword>Four Color Algorithm</keyword></descKeys><resConst><Consts><useLimit>Results are not guaranteed if there are multipart polygons in the data.</useLimit></Consts></resConst></dataIdInfo><distInfo><distributor><distorFormat><formatName>ArcToolbox Tool</formatName></distorFormat></distributor></distInfo></metadata>