diff --git a/src/chart_types/partition_chart/layout/viewmodel/fill_text_layout.ts b/src/chart_types/partition_chart/layout/viewmodel/fill_text_layout.ts
index 4e6a227031..b943550d14 100644
--- a/src/chart_types/partition_chart/layout/viewmodel/fill_text_layout.ts
+++ b/src/chart_types/partition_chart/layout/viewmodel/fill_text_layout.ts
@@ -30,8 +30,8 @@ import {
   wrapToTau,
 } from '../../../../common/geometry';
 import { logarithm } from '../../../../common/math';
-import { integerSnap, monotonicHillClimb } from '../../../../common/optimize';
 import { Box, Font, PartialFont, TextMeasure, VerticalAlignments } from '../../../../common/text_utils';
+import { integerSnap, monotonicHillClimb } from '../../../../solvers/monotonic_hill_climb';
 import { ValueFormatter } from '../../../../utils/common';
 import { Layer } from '../../specs';
 import { Config, Padding } from '../types/config_types';
diff --git a/src/common/color_calcs.test.ts b/src/common/color_calcs.test.ts
index 48e3f2e5fc..c9c27cb436 100644
--- a/src/common/color_calcs.test.ts
+++ b/src/common/color_calcs.test.ts
@@ -17,8 +17,8 @@
  * under the License.
  */
 
+import { integerSnap, monotonicHillClimb } from '../solvers/monotonic_hill_climb';
 import { makeHighContrastColor, combineColors } from './color_calcs';
-import { integerSnap, monotonicHillClimb } from './optimize';
 
 describe('calcs', () => {
   describe('test makeHighContrastColor', () => {
diff --git a/src/common/text_utils.ts b/src/common/text_utils.ts
index e8381ec5b0..1cf4800727 100644
--- a/src/common/text_utils.ts
+++ b/src/common/text_utils.ts
@@ -20,9 +20,9 @@
 import { $Values as Values } from 'utility-types';
 
 import { ArrayEntry } from '../chart_types/partition_chart/layout/utils/group_by_rollup';
+import { integerSnap, monotonicHillClimb } from '../solvers/monotonic_hill_climb';
 import { Datum } from '../utils/common';
 import { Pixels } from './geometry';
-import { integerSnap, monotonicHillClimb } from './optimize';
 
 /** @public */
 export const FONT_VARIANTS = Object.freeze(['normal', 'small-caps'] as const);
diff --git a/src/common/optimize.ts b/src/solvers/monotonic_hill_climb.ts
similarity index 100%
rename from src/common/optimize.ts
rename to src/solvers/monotonic_hill_climb.ts
diff --git a/src/solvers/screenspace_marker_scale_compressor.ts b/src/solvers/screenspace_marker_scale_compressor.ts
new file mode 100644
index 0000000000..8c207416a3
--- /dev/null
+++ b/src/solvers/screenspace_marker_scale_compressor.ts
@@ -0,0 +1,65 @@
+/*
+ * Licensed to Elasticsearch B.V. under one or more contributor
+ * license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright
+ * ownership. Elasticsearch B.V. licenses this file to you under
+ * the Apache License, Version 2.0 (the "License"); you may
+ * not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing,
+ * software distributed under the License is distributed on an
+ * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.  See the License for the
+ * specific language governing permissions and limitations
+ * under the License.
+ */
+
+import { Cartesian, Pixels, Ratio } from '../common/geometry';
+
+/** @internal */
+export type ArrayIndex = number;
+
+/** @internal */
+export interface ScaleCompression {
+  bounds: ArrayIndex[];
+  scaleMultiplier: Ratio;
+}
+
+/**
+ * A set of Cartesian positioned items with screenspace size (eg. axis tick labels, or scatterplot points) are represented as:
+ *   - a column vector of Cartesian positions in the domain (can be any unit)
+ *   - a column vector of screenspace size (eg. widths in pixels) which has the same number of elements
+ * The available room in the same screenspace units (practically, pixels) is supplied.
+ *
+ * Returns the scale multiplier, as well as the index of the elements determining (compressing) the scale, if solvable.
+ * If not solvable, it returns a non-finite number in `scaleMultiplier` and no indices in `bounds`.
+ * @internal
+ */
+export const screenspaceMarkerScaleCompressor = (
+  domainPositions: Cartesian[],
+  itemWidths: Pixels[],
+  outerWidth: Pixels,
+): ScaleCompression => {
+  const result: ScaleCompression = { bounds: [], scaleMultiplier: Infinity };
+  const itemCount = Math.min(domainPositions.length, itemWidths.length);
+  for (let left = 0; left < itemCount; left++) {
+    for (let right = 0; right < itemCount; right++) {
+      if (domainPositions[left] > domainPositions[right]) continue; // must adhere to left <= right
+
+      const range = outerWidth - itemWidths[left] / 2 - itemWidths[right] / 2; // negative if not enough room
+      const domain = domainPositions[right] - domainPositions[left]; // always non-negative and finite
+      const scaleMultiplier = range / domain; // may not be finite, and that's OK
+
+      if (scaleMultiplier < result.scaleMultiplier || Number.isNaN(scaleMultiplier)) {
+        result.bounds[0] = left;
+        result.bounds[1] = right;
+        result.scaleMultiplier = scaleMultiplier; // will persist a Number.finite() value for solvable pairs
+      }
+    }
+  }
+
+  return result;
+};