Reviewer assignment algorithm. I'm not sure this actually can generate all possible legal combinations of assignments but it's pretty random and only generates legal assignments. I'm also not sure it can't. First version is mostly procedural. Second one is heavy on streams.

Reviewers.java

import static java.util.stream.Collectors.joining;

import java.io.*;
import java.nio.file.*;
import java.util.*;
import java.util.stream.*;

public record Reviewers(List<String> handles) {
  //////////////////////////////////////////////////////////////////////////////
  // Utility methods

  // Return a randomly shuffled copy of a list
  private <T> List<T> shuffled(List<T> ts) {
    List<T> copy = new ArrayList<>(ts);
    Collections.shuffle(copy);
    return copy;
  }

  // Return a list of integers in the range [start, end)
  private List<Integer> numbers(int start, int end) {
    return IntStream.range(start, end).boxed().toList();
  }

  //////////////////////////////////////////////////////////////////////////////
  // Actual reviewer assignment

  public Map<String, List<String>> assignments(int n) {
    var shuffled = shuffled(handles);
    var rotations = shuffled(numbers(1, shuffled.size())).subList(0, n);
    var assignments = new HashMap<String, List<String>>();

    for (var i = 0; i < shuffled.size(); i++) {
      for (var r : rotations) {
        assignments
          .computeIfAbsent(shuffled.get(i), k -> new ArrayList<>())
          .add(shuffled.get((i + r) % shuffled.size()));
      }
    }
    return assignments;
  }

  //////////////////////////////////////////////////////////////////////////////
  // Output

  public void tsv(int n) {
    var m = assignments(n);
    for (var h : handles) {
      System.out.println(h + "\t" + m.get(h).stream().collect(joining("\t")));
    }
  }

  public static void main(String[] args) throws IOException {
    var handles = Files.lines(Path.of(args[0])).toList();
    var n = Integer.parseInt(args[1]);
    new Reviewers(handles).tsv(n);
  }
}

Reviewers2.java

import static java.util.stream.Collectors.groupingBy;
import static java.util.stream.Collectors.joining;
import static java.util.stream.Collectors.mapping;
import static java.util.stream.Collectors.toList;

import java.io.*;
import java.nio.file.*;
import java.util.*;
import java.util.stream.*;

public record Reviewers2(List<String> handles) {
  //////////////////////////////////////////////////////////////////////////////
  // Utility methods

  // Return a randomly shuffled copy of a list
  private <T> List<T> shuffled(List<T> ts) {
    List<T> copy = new ArrayList<>(ts);
    Collections.shuffle(copy);
    return copy;
  }

  // Return a list of integers in the range [start, end)
  private List<Integer> numbers(int start, int end) {
    return IntStream.range(start, end).boxed().toList();
  }

  //////////////////////////////////////////////////////////////////////////////
  // Actual reviewer assignment

  public Map<String, List<String>> assignments(int n) {
    var hs = shuffled(handles);
    var rs = shuffled(numbers(1, hs.size())).subList(0, n);

    record Pair(String author, String reviewer) {}

    return numbers(0, hs.size())
      .stream()
      .flatMap(i -> rs.stream().map(r -> new Pair(hs.get(i), hs.get((i + r) % hs.size()))))
      .collect(groupingBy(Pair::author, mapping(Pair::reviewer, toList())));
  }

  //////////////////////////////////////////////////////////////////////////////
  // Output

  public void tsv(int n) {
    var m = assignments(n);
    for (var h : handles) {
      System.out.println(h + "\t" + m.get(h).stream().collect(joining("\t")));
    }
  }

  public static void main(String[] args) throws IOException {
    var handles = Files.lines(Path.of(args[0])).toList();
    var n = Integer.parseInt(args[1]);
    new Reviewers(handles).tsv(n);
  }
}