diff --git a/src/main/java/Presenter/Algorithms/LeastMedianOfSquaresEstimator.java b/src/main/java/Presenter/Algorithms/LeastMedianOfSquaresEstimator.java
index 5b6a787..816e4ff 100644
--- a/src/main/java/Presenter/Algorithms/LeastMedianOfSquaresEstimator.java
+++ b/src/main/java/Presenter/Algorithms/LeastMedianOfSquaresEstimator.java
@@ -19,9 +19,9 @@ public class LeastMedianOfSquaresEstimator extends Algorithm {
     private LinkedList<Point> intersections = new LinkedList<>();
     private int n;
     private double quantileError;
-    private double kPlus;
-    private double kMinus;
-    private ArrayDeque<Slab> slabs;
+    private int kPlus;
+    private int kMinus;
+    private PriorityQueue<Slab> slabs;
     private Slab subSlabU1;
     private Slab subSlabU2;
     private Line sigmaMin;
@@ -31,51 +31,78 @@ public class LeastMedianOfSquaresEstimator extends Algorithm {
     public LeastMedianOfSquaresEstimator(LinkedList<Line> set, LinkedList<Point> intersections) {
         this.set = set;
         this.intersections = intersections;
+
+        //(1.) Let n <- |S|; q+ <- q; q- <- q+ * (1 - quantileError);....
+        n = set.size();
+        double quantile = 0.5;
+        double qPlus = quantile;
+        double qMinus = qPlus * (1 - quantileError);
+        kMinus = (int) Math.ceil(n * qMinus);
+        kPlus = (int) Math.ceil(n * qPlus);
     }
 
     public void printResult(){
-        System.out.println("RESULT: "+sigmaMin.getM()+"x +"+sigmaMin.getB());
+        System.out.println("RESULT: X1: "+sigmaMin.getX1() + ", X2: "+sigmaMin.getX2()+"\t Y1: "+sigmaMin.getY1()+", Y2: "+sigmaMin.getY2());
     }
 
     /**
      *
      */
     public void approximateLMS() {
-        //(1.) Let n <- |S|; q+ <- q; q- <- q+ * (1 - quantileError);....
-        n = set.size();
-        double quantile = 0.5;
-        double qPlus = quantile;
-        double qMinus = qPlus * (1 - quantileError);
-        kMinus = Math.ceil(n * qMinus);
-        kPlus = Math.ceil(n * qPlus);
+
 
         //(2.) Let U <- (-inf, inf) be the initial active slabs...
-        slabs = new ArrayDeque<>();
+        Comparator<Slab> comparator = new Comparator<Slab>() {
+            @Override
+            public int compare(Slab o1, Slab o2) {
+                if (o1.getDistance() < o2.getDistance())
+                    return -1;
+                if (o1.getDistance() > o2.getDistance())
+                    return 1;
+                else
+                    return 0;
+            }
+        };
+        slabs = new PriorityQueue<>(comparator);
         slabs.add(new Slab(-100000, 100000));
         heightsigmaMin = Double.MAX_VALUE;
 
         //(3.) Apply the following steps as long as the exists active slabs
-        while (!slabs.isEmpty()) {
-            Slab slab = slabs.getFirst();
-            //(a.) Select any active Slab and calc. the inversions
-            int numberOfIntersections = countInversions(slab);
+        boolean active = true;
+        Slab slab;
+        while (!this.slabs.isEmpty()) {
+            slab = this.slabs.peek();
+            if (slab.getActivity()){
+                //(a.) Select any active Slab and calc. the inversions
+                int numberOfIntersections = countInversions(slab);
 
-            //(b.) apply plane sweep
-            int constant = 1;
-            if (numberOfIntersections < (constant * n)) {
-                sigmaMin = planeSweep(slab);
-            } else {//(c.) otherwise....
-                //get random intersections point...
-                splitActiveSlab(intersectionsPoint, slab);
+                //(b.) apply plane sweep
+                int constant = 1;
+                if ((constant * n) >= numberOfIntersections) {
+                    sigmaMin = planeSweep(slab);
+                } else {//(c.) otherwise....
+                    //get random intersections point...
+                    splitActiveSlab(intersectionsPoint, slab);
+
+                    //(d.) this may update sigma min
+                    upperBound(intersectionsPoint);
+                    //(e.) for i={1,2}, call lower bound(Ui)
+                    lowerBound(subSlabU1);
+                    lowerBound(subSlabU2);
+
+                    if (subSlabU1.getActivity()){
+                        this.slabs.add(subSlabU1);
+                    }
+                    if (subSlabU2.getActivity()){
+                        this.slabs.add(subSlabU2);
+                    }
+                }
+            } else {
+                this.slabs.remove(slab);
             }
-            //(d.) this may update sigma min
-            upperBound(intersectionsPoint);
-            //(e.) for i={1,2}, call lower bound(Ui)
-            lowerBound(subSlabU1);
-            lowerBound(subSlabU2);
-        }
 
-//        printResult();
+
+        }
     }
 
     /**
@@ -98,13 +125,16 @@ public class LeastMedianOfSquaresEstimator extends Algorithm {
         numberOfInversions = mergeSort(umin, 0, umin.size() - 1, umax);
 
         for (Point point : intersections) {
-            if (point.getX() >= slab.getLower() && point.getX() < slab.getUpper()) {
+            if (point.getX() > slab.getLower() && point.getX() < slab.getUpper()) {
                 randomIntersection.add(point.getX());
             }
         }
 
         Collections.shuffle(randomIntersection);
-        intersectionsPoint = randomIntersection.get(0);
+        int access = (int) ( randomIntersection.size() * 0.5);
+        if (!randomIntersection.isEmpty()){
+            intersectionsPoint = randomIntersection.get(access);
+        }
 
         return numberOfInversions;
     }
@@ -112,12 +142,14 @@ public class LeastMedianOfSquaresEstimator extends Algorithm {
     //Parameter anpassen
 
     /**
-     *
-     * @param a
-     * @param start
-     * @param end
-     * @param aux
-     * @return
+     * Angepasster Merge-Sort Algorithmus.
+     * Die Funktion bekommt neben den standard Parametern zusätzlich eine Liste mit Elementen
+     * die als Groundtruth dienen.
+     * @param a Eingabefeld mit den Elementen die überprüft werden sollen.
+     * @param start Startpunkt des Eingabefeldes.
+     * @param end   Endpunkt des Eingabefeldes.
+     * @param aux   Groundtruth Ordnung um die Anzahl der Inversionen zu bestimmen.
+     * @return  Anzahl der inversionen zwischen a und aux.
      */
     public int mergeSort(List<Double> a, int start, int end, List<Double> aux) {
         if (start >= end) {
@@ -169,61 +201,70 @@ public class LeastMedianOfSquaresEstimator extends Algorithm {
         double heightOfBracelet = heightsigmaMin;
 
         for (Point current : xQueue){
-           double[] currentBracelet = calcKMinusBracelet(current);
+            Double[] currentBracelet = calcKMinusBracelet(current, kMinus);
 
             if (currentBracelet == null){
                 continue;
             } else if (currentBracelet[0] < heightOfBracelet){
                 heightOfBracelet = currentBracelet[0];
                 bracelet = new Line(current.getX(), current.getX(), currentBracelet[1], currentBracelet[2]);
-                System.out.println("R: "+bracelet.getM()+"x +"+bracelet.getB());
             }
         }
 
-
+        slab.setActivity(false);
         return bracelet;
     }
 
     /**
-     * @param point
+     * Diese Methode spaltet den aktiven Slab an der x Koordinate point. Es werden zwei neue Slabs erzeugt.
+     * @param point x Koordinate an der, der Split geschieht.
      */
     public void splitActiveSlab(double point, Slab active) {
-
         subSlabU1 = new Slab(active.getLower(), point);
         subSlabU2 = new Slab(point, active.getUpper());
-        this.slabs.removeFirst();
+
+        this.slabs.remove(active);
     }
 
     /**
+     *
      * @param point
      */
     public void upperBound(double point) {
 
-        double height;
-
+        double height = heightsigmaMin;
+        double tmpHeight;
         ArrayList<Double> sortedLineSequence = getEjValues(point);
 
-        for (int i = 1; i < (n - (kMinus + 1)); i++) {
-            height = sortedLineSequence.get(i + (((int) kMinus) - 1)) - sortedLineSequence.get(i);
+
+        int itnbr = ((n - kMinus) + 1);
+        for (int i = 0; i < itnbr; i++) {
+            tmpHeight = sortedLineSequence.get((i + kMinus) - 1) - sortedLineSequence.get(i);
+            if (tmpHeight < height){
+                height = tmpHeight;
+            }
 
             if (height < heightsigmaMin) {
-                sigmaMin.setEndPoints(point, sortedLineSequence.get(i + (((int) kMinus) - 1))
-                                     ,point, sortedLineSequence.get(i));
+                heightsigmaMin = height;
+                if (sigmaMin != null){
+                sigmaMin.setEndPoints(point, sortedLineSequence.get(i)
+                                     ,point, sortedLineSequence.get((i + kMinus) - 1));
+                } else {
+                    sigmaMin = new Line(point, point, sortedLineSequence.get(i), sortedLineSequence.get((i + kMinus) - 1));
+                }
             }
         }
 
     }
 
     /**
-     * @param slab
+     * @param pslab
      * @return
      */
-    public void lowerBound(Slab slab) {
+    public void lowerBound(Slab pslab) {
 
         int[] alpha = new int[n];
         int[] beta = new int[n];
-        alpha[0] = 0;
-        beta[0] = 0;
         int strictlyGreater = 0;
 
         //Teil I.
@@ -231,50 +272,62 @@ public class LeastMedianOfSquaresEstimator extends Algorithm {
         ArrayList<Double> uminList;
 
         //y koordinaten der Schnittpunkte
-        ArrayList<Point> lines = new ArrayList<>();
-        System.out.println("Anzahl der Slabs: "+this.slabs.size());
+        ArrayList<Line> lines = new ArrayList<>();
         for (Line p : set) {
-            lines.add(new Point(((slab.getLower() * p.getM()) + p.getB()), ((slab.getUpper() * p.getM()) + p.getB())));
+            lines.add(new Line(pslab.getLower(), pslab.getUpper(),((pslab.getLower() * p.getM()) + p.getB()), ((pslab.getUpper() * p.getM()) + p.getB())));
         }
 
+        umaxList = getEjValues(pslab.getUpper());
+        uminList = getEjValues(pslab.getLower());
 
-        umaxList = getEjValues(slab.getUpper());
-        uminList = getEjValues(slab.getLower());
-
-        for (int i = 1; i < n; i++) {
-            Point level = new Point(uminList.get(i), umaxList.get(i));
-            for (Point point : lines) {
-                if ((point.getX() < level.getX()) && (point.getY() < level.getY())) {
+        for (int i = 0; i < n; i++) {
+            Line level = new Line(pslab.getLower(),pslab.getUpper(),uminList.get(i), umaxList.get(i));
+            for (Line line : lines) {
+                if ((line.getY1() < level.getY1()) && (line.getY2() < level.getY2())) {
                     alpha[i]++;
                 }
 
-                if ((point.getX() > level.getX()) && (point.getY() > level.getY())) {
+                if ((line.getY1() > level.getY1()) && (line.getY2() > level.getY2())) {
                     strictlyGreater++;
                 }
             }
             beta[i] = n - (alpha[i] + strictlyGreater);
+            strictlyGreater = 0;
         }
+        //TEST der Alpha und Beta werte, siehe JUnit Test
+        //for (int i=0;i<alpha.length;i++){
+        //    System.out.println("Alpha["+i+"]: "+alpha[i]+"\t Beta["+i+"]: "+beta[i]);
+        //}
+        //Test
 
         //Teil II.
-        int i = 1;
-        double h = Double.MAX_VALUE;
-        for (int j = 1; j < n; j++) {
-            while (((i < n) && (Math.abs(beta[i] - alpha[j]) < kPlus))){
-                System.out.println("i: "+i+"\t "+Math.abs(beta[i] - alpha[j])+"\t kPlus: "+kPlus);
+        int i = 0;
+        double h;
+        pslab.setActivity(false);
+        for (int j = 0; j < n; j++) {
+            while ((i < n && (Math.abs(beta[i] - alpha[j]) < kPlus))){
                 i++;
             }
+            //test
+            //if (i < n)
+            //    System.out.println("i: "+i+", j:"+j+"\t "+Math.abs(beta[i] - alpha[j])+"\t kPlus: "+kPlus);
 
             if (i >= n) {
+                //System.out.println("i: "+i+", j:"+j+". ungültig");
+                pslab.setActivity(false);
                 break;
             } else {
-                h = Math.min((uminList.get(j) - uminList.get(i)), (umaxList.get(j) - umaxList.get(i)));
+                h = Math.min(Math.abs(uminList.get(j) - uminList.get(i)), Math.abs(umaxList.get(j) - umaxList.get(i)));
+                double error = 0.01;
+                if (((1 + error) * h) < heightsigmaMin) {
+                    //System.out.println("h: "+ h +" ist kleiner als height(sigmaMin): "+heightsigmaMin);
+                    pslab.setActivity(true);
+                    return;
+                }
             }
+            i = 0;
         }
-        double error = 0.01;
-        System.out.println("h: "+h);
-        if (((1 + error) * h) < heightsigmaMin) {
-            this.slabs.addLast(slab);
-        }
+
     }
 
     /**
@@ -298,24 +351,26 @@ public class LeastMedianOfSquaresEstimator extends Algorithm {
     }
 
     /**
-     *
-     * @param x
-     * @return
+     * Die Funktion berechnet anhand einer vertikalen Gerade x = px das sogenannte kleinste kMinus Bracelet.
+     * Mit anderen Worten es wird eine vertikale Teilgerade berechnet die mindestens kMinus Geraden schneidet
+     * und dabei minimal ist.
+     * @param px Koordinate um die "vertikale Gerade" zu simulieren.
+     * @return Das Array enthält höhe des Bracelet, e_j und e_(j + kMinus - 1)
      */
-    public double[] calcKMinusBracelet(Point x) {
+    public Double[] calcKMinusBracelet(Point px, int kMinusValue) {
 
         //y Koordinaten für das kMinus brecalet
         LinkedList<Double> intersections = new LinkedList<>();
         for (Line line : set) {
-            intersections.add((x.getX() * line.getM())+line.getB());
+            intersections.add((px.getX() * line.getM())+line.getB());
         }
-        if (intersections.size() < kMinus){
-            return null;
-        } else {
+        if (intersections.size() >= kMinusValue){
             Collections.sort(intersections);
-            double height = Math.abs(intersections.getFirst() - intersections.getLast());
-            double[] ret = {height, intersections.getFirst(), intersections.getLast()};
+            double height = Math.abs(intersections.get(0) - intersections.get(0 + kMinusValue - 1));
+            Double[] ret = {height, intersections.get(0), intersections.get(0 + kMinusValue - 1)};
             return ret;
+        } else {
+            return  null;
         }
 
     }
@@ -324,7 +379,7 @@ public class LeastMedianOfSquaresEstimator extends Algorithm {
      * Hilfsklasse um die Slabs zu verteilen, private Klasse da sonst nicht verwendett wird und somit eine
      * äußere Klasse überflüssig ist...
      */
-    private static class Slab {
+    protected static class Slab {
         private double upper;
         private double lower;
         private Boolean activity;
@@ -332,6 +387,7 @@ public class LeastMedianOfSquaresEstimator extends Algorithm {
         public Slab(double lower, double upper) {
             this.upper = upper;
             this.lower = lower;
+            this.activity = true;
         }
 
         public Boolean getActivity() {
@@ -358,5 +414,103 @@ public class LeastMedianOfSquaresEstimator extends Algorithm {
             this.lower = lower;
         }
 
+        public Double getDistance(){
+
+            return Math.abs(this.upper - this.lower);
+        }
+
+    }
+
+
+    /**
+     * Im Allgemeinen werden keine Getter und Setter Methoden benötigt aber sie sind nützlich bei den JUnit Testfällen.
+     */
+
+    public LinkedList<Line> getSet() {
+        return set;
+    }
+
+    public void setSet(LinkedList<Line> set) {
+        this.set = set;
+    }
+
+    public LinkedList<Point> getIntersections() {
+        return intersections;
+    }
+
+    public void setIntersections(LinkedList<Point> intersections) {
+        this.intersections = intersections;
+    }
+
+    public int getN() {
+        return n;
+    }
+
+    public void setN(int n) {
+        this.n = n;
+    }
+
+    public double getQuantileError() {
+        return quantileError;
+    }
+
+    public void setQuantileError(double quantileError) {
+        this.quantileError = quantileError;
+    }
+
+    public int getkPlus() {
+        return kPlus;
+    }
+
+    public void setkPlus(int kPlus) {
+        this.kPlus = kPlus;
+    }
+
+    public int getkMinus() {
+        return kMinus;
+    }
+
+    public void setkMinus(int kMinus) {
+        this.kMinus = kMinus;
+    }
+
+    public Slab getSubSlabU1() {
+        return subSlabU1;
+    }
+
+    public void setSubSlabU1(Slab subSlabU1) {
+        this.subSlabU1 = subSlabU1;
+    }
+
+    public Slab getSubSlabU2() {
+        return subSlabU2;
+    }
+
+    public void setSubSlabU2(Slab subSlabU2) {
+        this.subSlabU2 = subSlabU2;
+    }
+
+    public Line getSigmaMin() {
+        return sigmaMin;
+    }
+
+    public void setSigmaMin(Line sigmaMin) {
+        this.sigmaMin = sigmaMin;
+    }
+
+    public double getHeightsigmaMin() {
+        return heightsigmaMin;
+    }
+
+    public void setHeightsigmaMin(double heightsigmaMin) {
+        this.heightsigmaMin = heightsigmaMin;
+    }
+
+    public double getIntersectionsPoint() {
+        return intersectionsPoint;
+    }
+
+    public void setIntersectionsPoint(double intersectionsPoint) {
+        this.intersectionsPoint = intersectionsPoint;
     }
 }
diff --git a/src/test/java/Presenter/Algorithms/LeastMedianOfSquaresEstimatorTest.java b/src/test/java/Presenter/Algorithms/LeastMedianOfSquaresEstimatorTest.java
index dea4976..829b910 100644
--- a/src/test/java/Presenter/Algorithms/LeastMedianOfSquaresEstimatorTest.java
+++ b/src/test/java/Presenter/Algorithms/LeastMedianOfSquaresEstimatorTest.java
@@ -8,6 +8,7 @@ import org.junit.Test;
 
 
 import java.util.ArrayList;
+import java.util.Collections;
 import java.util.LinkedList;
 
 import static org.junit.Assert.*;
@@ -26,12 +27,19 @@ public class LeastMedianOfSquaresEstimatorTest {
     @Before
     public void setUp() throws Exception {
 
-        LinkedList<Line> line = new LinkedList<>();
+        Double[] x = {18d,24d,30d,34d,38d};
+        Double[] y = {18d,26d,30d,40d,70d};
+
+        LinkedList<Line> lines = new LinkedList<>();
         LinkedList<Point> intersections = new LinkedList<>();
 
+        for (int i=0; i<5; i++)
+            lines.add(new Line(x[i], y[i]));
 
 
-        lms = new LeastMedianOfSquaresEstimator(line, intersections);
+
+
+        lms = new LeastMedianOfSquaresEstimator(lines, intersections);
     }
 
     @Test
@@ -62,4 +70,55 @@ public class LeastMedianOfSquaresEstimatorTest {
 
     }
 
+    @Test
+    public void geEjValues() throws Exception {
+
+        Double[] expected = {36d,50d,60d,74d,108d};
+        ArrayList<Double> actual =  lms.getEjValues(1d);
+        assertArrayEquals(expected, actual.toArray());
+    }
+
+    @Test
+    public void calcKMinusBracelet() throws Exception {
+
+        Point point = new Point(1d, 1d);
+        Double[] expected = {24d, 36d, 60d};
+        Double[] actual   = lms.calcKMinusBracelet(point, 3);
+
+        assertArrayEquals(expected, actual);
+
+    }
+
+    @Test
+    public void upperBound() throws Exception {
+        lms.setkMinus(3);
+        lms.setHeightsigmaMin(500);
+        lms.setSigmaMin(new Line(0,0,0,0));
+
+        Line expected = new Line(5,5,146,210);
+        lms.upperBound(5d);
+
+        assertEquals(expected.getX1(), lms.getSigmaMin().getX1(),0.01);
+        assertEquals(expected.getX2(), lms.getSigmaMin().getX2(),0.01);
+        assertEquals(expected.getY1(), lms.getSigmaMin().getY1(),0.01);
+        assertEquals(expected.getY2(), lms.getSigmaMin().getY2(),0.01);
+    }
+
+    @Test
+    public void lowerBound() throws Exception {
+        //kann nur über sout geprüft werden test passt aber
+        Double[] expectedAlpha = {0d,0d,0d,2d,4d};
+        Double[] expectedBeta  = {2d,4d,4d,2d,1d};
+        lms.setHeightsigmaMin(500);
+
+        LeastMedianOfSquaresEstimator.Slab slab = new LeastMedianOfSquaresEstimator.Slab(-2,0);
+        lms.lowerBound(slab);
+        assertTrue(slab.getActivity());
+    }
+
+    @Test
+    public void planeSweep() throws Exception {
+
+    }
+
 }
\ No newline at end of file