From Bellman–Ford to Near-Linear SSSP with IoT/IIoT + GIS

Graph Intelligence for Mining & Fossil Fuels

Shortest-Path methods—Bellman–Ford, Dijkstra, and modern near-linear SSSP—become real-time decision engines when fused with IoT/IIoT telemetry and GIS. This post shows a practical architecture and a runnable, minimal Python example for haul routing, pipeline isolation and time-expanded scheduling.

IoT/IIoT GIS & DEM Bellman–Ford Dijkstra Near-Linear SSSP Time-Expanded Graph Mining Logistics Pipelines

1) Industry graph: nodes, edges, weights

Nodes

• Pits/benches, shovels, crushers, stockpiles
• Wells, pads, manifolds, compressors
• Road segments, ramps, conveyors, valve stations
• Sensors: GPS, pressure, vibration, temp, flow
• Context: weather cells, permits/blocks, substations

Edges

• Connectivity: roads, belts, pipes (directional)
• Time links: state at t → t+Δ (queues/windows)
• Process dependencies: blast→load→haul→crush

Weights (multi-objective)

• Travel time, fuel, tyre/wear, CO₂e
• Risk: slope, geotech, weather, H₂S
• Throughput penalties, maintenance windows

2) Where SSSP fits

• Haul routing: bench → crusher with slope & congestion penalties (Dijkstra or near-linear SSSP).
• Pipeline isolation: fastest-safe valve closures during leaks (Dijkstra; Bellman–Ford if using negative credits).
• Shift/schedule: time-expanded tasks with windows; repeated relaxations favor BF.

3) IoT/IIoT + GIS → dynamic graph weights

Ingest: MQTT/Kafka (truck CAN bus, PLC/OPC UA, PI historians), RTK GPS, DEM slope (PostGIS/ArcGIS), weather. Map to edges: grade→speed cap; rain→rolling resistance; GPS density→congestion; geotech→risk. Update: stream joins recalc weights each minute.

4) Compact architecture diagram

Pipeline: Sensors → Streams → Feature/weights (+GIS) → Graph → SSSP → Dispatch.

5) KPI deltas to monitor

−5–12% haul cycle time

−4–10% fuel/ton & CO₂e/ton

−3–8% tyre & wear cost

↓ MTTI (pipeline isolation) & queue time

6) Minimal, runnable Python demo

#!/usr/bin/env python3

from collections import defaultdict

import heapq

# IoT/IIoT synthetic edge data

iot_edges = {

    ("Bench","Ramp"):   {"base":4.0, "slope":8,  "rain":2, "cong":0.1},

    ("Ramp","Haul1"):   {"base":3.0, "slope":5,  "rain":0, "cong":0.3},

    ("Haul1","Crusher"):{ "base":6.0, "slope":2, "rain":5, "cong":0.2},

    ("Ramp","Bypass"):  {"base":5.0, "slope":1,  "rain":0, "cong":0.0},

    ("Bypass","Crusher"):{ "base":6.5,"slope":1, "rain":0, "cong":0.05},

}

def edge_cost(params, carbon_price=0.0, credit=0.0):

    t = params["base"]

    t += 0.04 * params["slope"]

    t += 0.02 * params["rain"]

    t += 2.0  * params["cong"]

    t += carbon_price

    t += credit

    return t

def time_expand(edges, steps=2):

    G = defaultdict(list)

    for (u,v), p in edges.items():

        for t in range(steps-1):

            u_t, v_t = f"{u}@t{t}", f"{v}@t{t+1}"

            w = edge_cost(p)

            G[u_t].append((v_t, w))

            G[f"{u}@t{t}"].append((f"{u}@t{t+1}", 0.5))

    return G

def dijkstra(G, s):

    dist, prev = {s:0.0}, {}

    pq = [(0.0, s)]

    while pq:

        d,u = heapq.heappop(pq)

        if d!=dist.get(u, float("inf")): continue

        for v,w in G.get(u,[]):

            nd = d + w

            if nd < dist.get(v, float("inf")):

                dist[v]=nd; prev[v]=u; heapq.heappush(pq,(nd,v))

    return dist, prev

def bellman_ford(G, s):

    nodes = list(G.keys()) + [v for u in G for v,_ in G[u]]

    nodes = list(dict.fromkeys(nodes))

    dist = {n: float("inf") for n in nodes}; dist[s]=0.0

    prev = {}

    for _ in range(len(nodes)-1):

        changed=False

        for u in nodes:

            for v,w in G.get(u,[]):

                if dist[u] + w < dist.get(v, float("inf")):

                    dist[v] = dist[u] + w; prev[v]=u; changed=True

        if not changed: break

    return dist, prev

def path(prev, t):

    P=[t]

    while t in prev: t=prev[t]; P.append(t)

    return list(reversed(P))

G = time_expand(iot_edges, steps=3)

start = "Bench@t0"; goal = "Crusher@t2"

dD, pD = dijkstra(G, start)

print("Dijkstra:", dD.get(goal), path(pD, goal))

G_credit = time_expand({**iot_edges, ("Ramp","Bypass"): {**iot_edges[("Ramp","Bypass")]}}, steps=3)

for u in list(G_credit.keys()):

    G_credit[u] = [(v, w-0.8 if u.startswith("Ramp@") and v.startswith("Bypass@") else w) for (v,w) in G_credit[u]]

dB, pB = bellman_ford(G_credit, start)

print("Bellman–Ford:", dB.get(goal), path(pB, goal))

7) Implementation blueprint (8–12 weeks)

1. Weeks 1–2: Data audit; DEM & road/pipe centerlines in PostGIS; integrate 2–3 live sensor topics from trucks/PLC.
2. Weeks 3–4: Build weight builder service; static Dijkstra prototype on a historical snapshot; create GIS dashboard.
3. Weeks 5–6: Develop time-expanded model; implement bucketed/near-linear SSSP for sparse graphs; replay last 7 days for validation.
4. Weeks 7–8: Integrate closed-loop route suggestions into fleet management/SCADA; conduct A/B testing on one pit or pipeline segment.
5. Weeks 9–12: Tune multi-objective weights (fuel, CO₂, risk); implement failover mechanisms; complete safety review and operational sign-off.

8) Tooling

• Streams: MQTT, Kafka, OPC UA
• Processing: Spark Structured Streaming, Flink
• GIS: PostGIS, QGIS/ArcGIS, pgRouting
• Graph: NetworkX/igraph (prototype); GraphBLAS, Boost, TigerGraph, Neo4j (production); Spark GraphFrames (batch)
• MLOps & QA: MLflow for model/weight tuning; Great Expectations for data quality checks

Ethics & scope note: This article and code are educational and generic. Avoid deploying without site-specific engineering and safety validation.

End of post.