{
  "title": "Why shared edges change a network-access decision",
  "disclosure": "New synthetic teaching companion, not the dissertation implementation or its research benchmark. Costs are invented units, not travel times or distances.",
  "metrics": [
    {
      "label": "Independent shortest-path union cost",
      "value": 12
    },
    {
      "label": "Minimum shared-network cost",
      "value": 10
    },
    {
      "label": "Exhaustively checked edge subsets",
      "value": 32
    }
  ],
  "tables": [
    {
      "heading": "Worked example: independent routes",
      "headers": [
        "Target",
        "Route",
        "Route cost"
      ],
      "rows": [
        [
          "T1",
          "S → T1",
          6
        ],
        [
          "T2",
          "S → T2",
          6
        ]
      ]
    },
    {
      "heading": "Worked example: selected shared-network edges",
      "headers": [
        "Edge",
        "Cost counted once"
      ],
      "rows": [
        [
          "H ↔ S",
          4
        ],
        [
          "H ↔ T1",
          3
        ],
        [
          "H ↔ T2",
          3
        ]
      ]
    },
    {
      "heading": "Measured synthetic micro-benchmark (environment-specific)",
      "headers": [
        "Targets",
        "Edges",
        "Subsets",
        "Path-union cost",
        "Shared cost",
        "Dijkstra median ms",
        "Exhaustive median ms"
      ],
      "rows": [
        [
          2,
          5,
          32,
          12,
          10,
          0.011,
          0.0548
        ],
        [
          3,
          9,
          512,
          18,
          13,
          0.0168,
          1.0468
        ],
        [
          4,
          13,
          8192,
          24,
          16,
          0.0228,
          21.8929
        ]
      ]
    }
  ],
  "notes": [
    "For each target the direct path costs 6, versus 7 through H. Yet sharing S–H gives a total selected-edge cost of 4 + 3 + 3 = 10 instead of 6 + 6 = 12. Individual journeys need not become shorter.",
    "The comparable baseline is the union of independent shortest-path edges, counted once. Summing journey costs would double-count any shared edge.",
    "Solver settings: simple undirected graphs; positive integer edge costs; all targets required; optional intermediate nodes; exhaustive enumeration of every subset; no pruning, tolerance, heuristic, random seed, external solver, or time limit; single process; hard cap 16 edges (65,536 subsets).",
    "Timings are medians of 5 runs after one warm-up, measured with perf_counter_ns, including validation and solving but excluding fixture creation, report assembly, and file I/O. They are illustrative, not a scalable algorithm comparison.",
    "Measured environment: CPython 3.12.14, Windows 11, AMD64. Workload and timing noise vary by machine; rerunning overwrites timings.",
    "This familiar minimum connecting-subgraph example is not a novelty claim, proof about the original formulation, or validation of convex-hull preprocessing. The public R source uses a separate OMPR/GLPK formulation with flow variables.",
    "No unpublished manuscript, employer code, client records, or real location data is included. No journal publication or DOI is asserted."
  ],
  "sources": [
    {
      "label": "Public research code, pinned revision",
      "url": "https://github.com/efkopru/gemini-shortest-path/tree/bc917f2a679f0ef624b15d2e6b4a3dc5fc8db388"
    },
    {
      "label": "UT Dallas doctoral record (Spring 2024)",
      "url": "https://graduate.utdallas.edu/fsa/doctoral-degrees-awarded/2023-2024-doctoral-degrees-awarded/"
    }
  ]
}