import java.io.*; import java.nio.charset.StandardCharsets; import java.nio.file.*; import java.util.*; public class LRMCSim { static final double EPSILON = 1e-6; static final int NUM_CLUSTERS = 10; static final double CLUSTER_FRACTION = 0.20; static final double PINTRA = 0.005; static final double PINTER = 0.00001; static final long SEED = 123456789L; static final int S_MIN = 10_000; static final int S_MAX = 1_000_000; static final int NUM_SIZES = 30; static final int TRIALS = 3; static final double[] DENSITY_SCALES = {0.5, 1.0, 2.0}; static final String[] SERIES_LABELS = {"dens_x0.5", "dens_x1.0", "dens_x2.0"}; static final boolean ECHO_CLIQUE2_OUTPUT = false; static final String EXTRA_HEAP = "-Xmx8g"; static String clique2Main; static String outputCsvFile; public static void main(String[] args) throws Exception { if (args.length < 2) { System.err.println("Usage: java LRMCSim "); return; } clique2Main = args[0]; outputCsvFile = args[1]; Random rng = new Random(SEED); List allRows = new ArrayList<>(); int[] sizes = logSpaced(S_MIN, S_MAX, NUM_SIZES); for (int si = 0; si < DENSITY_SCALES.length; si++) { double scale = DENSITY_SCALES[si]; String series = SERIES_LABELS[si]; for (int n : sizes) { Path inputFile = Files.createTempFile("clique2_input_" + series + "_n" + n + "_", ".txt"); inputFile.toFile().deleteOnExit(); long m = generateClusteredGraphToFile( n, NUM_CLUSTERS, CLUSTER_FRACTION, PINTRA * scale, PINTER * scale, rng, inputFile); double theoX = (n + m) * Math.log(Math.max(2, n)); for (int t = 0; t < TRIALS; t++) { double ms = runClique2(EPSILON, inputFile); allRows.add(new Row(series, n, m, t + 1, ms, theoX, 0)); } } } double num = 0, den = 0; for (Row r : allRows) { num += r.theoX * r.ms; den += r.theoX * r.theoX; } double k = den == 0 ? 0 : num / den; // Write CSV to specified file try (BufferedWriter writer = Files.newBufferedWriter(Paths.get(outputCsvFile), StandardCharsets.UTF_8)) { writer.write("series,n,m,trial,ms,theo_x,normalized_theory_ms\n"); for (Row r : allRows) { double norm = k * r.theoX; writer.write(String.format(Locale.US, "%s,%d,%d,%d,%.3f,%.3f,%.3f\n", r.series, r.n, r.m, r.trial, r.ms, r.theoX, norm)); } } // Optional: also echo summaries to stdout Map>> bySeriesSize = new TreeMap<>(); for (Row r : allRows) { bySeriesSize.computeIfAbsent(r.series, s -> new TreeMap<>()) .computeIfAbsent(r.n, _k -> new ArrayList<>()).add(r); } for (var eSeries : bySeriesSize.entrySet()) { String s = eSeries.getKey(); for (var e : eSeries.getValue().entrySet()) { int n = e.getKey(); long m = e.getValue().get(0).m; double[] arr = e.getValue().stream().mapToDouble(rr -> rr.ms).toArray(); double mean = mean(arr), sd = stddev(arr, mean); double theoX = e.getValue().get(0).theoX; double norm = k * theoX; System.out.printf(Locale.US, "# summary,%s,%d,%d,%.3f,%.3f,%.3f%n", s, n, m, mean, theoX, norm); if (TRIALS > 1) { System.out.printf(Locale.US, "# summary_std,%s,%d,%d,%.3f%n", s, n, m, sd); } } } } // Run L-RMC Algorithm private static double runClique2(double epsilon, Path inputFile) throws IOException, InterruptedException { String javaBin = System.getProperty("java.home") + File.separator + "bin" + File.separator + "java"; String classpath = System.getProperty("java.class.path"); List cmd = new ArrayList<>(); cmd.add(javaBin); cmd.add(EXTRA_HEAP); cmd.add("-cp"); cmd.add(classpath); cmd.add(clique2Main); cmd.add(Double.toString(epsilon)); cmd.add(inputFile.toAbsolutePath().toString()); ProcessBuilder pb = new ProcessBuilder(cmd); pb.redirectErrorStream(true); Process p = pb.start(); String lastRuntime = null; try (BufferedReader br = new BufferedReader( new InputStreamReader(p.getInputStream(), StandardCharsets.UTF_8))) { String line; while ((line = br.readLine()) != null) { if (ECHO_CLIQUE2_OUTPUT) System.out.println(line); if (line.startsWith("Runtime:")) lastRuntime = line; } } int exit = p.waitFor(); if (exit != 0) throw new RuntimeException("clique2 exited with code " + exit); if (lastRuntime == null) throw new RuntimeException("No 'Runtime: ... ms' line from clique2"); String msStr = lastRuntime.replace("Runtime:", "").replace("ms", "").trim(); return Double.parseDouble(msStr); } // Clustered Generator (expected O(m)) static long generateClusteredGraphToFile( int n, int k, double frac, double pIntra, double pInter, Random rng, Path outFile) throws IOException { int clusterTotal = (int) Math.round(frac * n); int[] nodes = new int[n]; for (int i = 0; i < n; i++) nodes[i] = i + 1; shuffle(nodes, rng); int base = clusterTotal / k, rem = clusterTotal % k; int[][] clusters = new int[k][]; int idx = 0; for (int i = 0; i < k; i++) { int sz = base + (i < rem ? 1 : 0); clusters[i] = Arrays.copyOfRange(nodes, idx, idx + sz); Arrays.sort(clusters[i]); idx += sz; } int[] background = Arrays.copyOfRange(nodes, idx, n); Arrays.sort(background); Path tmpEdges = Files.createTempFile("edges_only_", ".txt"); tmpEdges.toFile().deleteOnExit(); long m = 0; try (BufferedWriter w = Files.newBufferedWriter(tmpEdges, StandardCharsets.UTF_8)) { for (int i = 0; i < k; i++) m += triPairsToWriter(clusters[i], pIntra, w, rng); for (int i = 0; i < k; i++) for (int j = i + 1; j < k; j++) m += rectPairsToWriter(clusters[i], clusters[j], pInter, w, rng); for (int i = 0; i < k; i++) m += rectPairsToWriter(clusters[i], background, pInter, w, rng); m += triPairsToWriter(background, pInter, w, rng); } try (BufferedWriter hdr = Files.newBufferedWriter(outFile, StandardCharsets.UTF_8, StandardOpenOption.CREATE, StandardOpenOption.TRUNCATE_EXISTING)) { hdr.write(n + " " + m); hdr.newLine(); } try (OutputStream out = Files.newOutputStream(outFile, StandardOpenOption.APPEND); InputStream in = Files.newInputStream(tmpEdges)) { byte[] buf = new byte[1 << 20]; int len; while ((len = in.read(buf)) != -1) out.write(buf, 0, len); } return m; } // skip-sampling over unordered pairs in a set static long triPairsToWriter(int[] set, double p, BufferedWriter w, Random rng) throws IOException { int s = set.length; if (s < 2 || p <= 0) return 0L; final double logq = Math.log(1.0 - p); long written = 0; int row = 0, off = -1; while (row < s - 1) { double r = rng.nextDouble(); int skip = (int) Math.floor(Math.log(1.0 - r) / logq); off += 1 + skip; while (row < s - 1 && off >= (s - row - 1)) { off -= (s - row - 1); row++; } if (row < s - 1) { int u = set[row], v = set[row + 1 + off]; w.write(u + " " + v); w.newLine(); written++; } } return written; } // skip-sampling over A x B static long rectPairsToWriter(int[] A, int[] B, double p, BufferedWriter w, Random rng) throws IOException { int a = A.length, b = B.length; if (a == 0 || b == 0 || p <= 0) return 0L; final double logq = Math.log(1.0 - p); long total = 1L * a * b, t = -1, written = 0; while (true) { double r = rng.nextDouble(); long skip = (long) Math.floor(Math.log(1.0 - r) / logq); t += 1 + skip; if (t >= total) break; int i = (int) (t / b), j = (int) (t % b); w.write(A[i] + " " + B[j]); w.newLine(); written++; } return written; } // Helpers static int[] logSpaced(int lo, int hi, int k) { double a = Math.log(lo), b = Math.log(hi); int[] out = new int[k]; for (int i = 0; i < k; i++) { double t = i / (double) (k - 1); out[i] = (int) Math.round(Math.exp(a + t * (b - a))); out[i] = Math.max(lo, Math.min(hi, (out[i] + 500) / 1000 * 1000)); // snap to nearest 1000 } for (int i = 1; i < k; i++) if (out[i] <= out[i - 1]) out[i] = out[i - 1] + 1000; out[k - 1] = hi; return out; } static void shuffle(int[] a, Random rng) { for (int i = a.length - 1; i > 0; i--) { int j = rng.nextInt(i + 1); int t = a[i]; a[i] = a[j]; a[j] = t; } } static double mean(double[] x) { double s = 0; for (double v : x) s += v; return s / x.length; } static double stddev(double[] x, double mean) { if (x.length <= 1) return 0; double s2 = 0; for (double v : x) { double d = v - mean; s2 += d * d; } return Math.sqrt(s2 / (x.length - 1)); } static final class Row { final String series; final int n; final long m; final int trial; final double ms; final double theoX; final double norm; Row(String series, int n, long m, int trial, double ms, double theoX, double norm) { this.series = series; this.n = n; this.m = m; this.trial = trial; this.ms = ms; this.theoX = theoX; this.norm = norm; } } }