Represent the battlespace with a time-expanded directed graph. Nodes capture sensor tracks, predicted drone waypoints, defended assets, batteries, and discrete intercept windows—space–time points where an effect could meet a target. Edges encode feasible temporal transitions under drone kinematics, terrain/line-of-sight, and communication relays. Edge costs are multi-objective: expected damage if un-intercepted, time-to-impact, effector kill probability, collateral/EMCON penalties, reload/thermal limits, and comms latency/risk. This provides a unified substrate for risk-aware routing and allocation without weapon-specific detail.
2) Why BF, Dijkstra, and the New SSSP Matter
Bellman–Ford tolerates arbitrary directed graphs and negative penalties (but not negative time), aligning well with time-expanded layers where many edges share timestamps. Its bulk relaxations naturally support rapid re-labeling when the picture changes (jamming, decoys). Dijkstra excels for static, non-negative costs, but the globally sorted frontier (priority queue) becomes the bottleneck at swarm scale. The new “sorting-barrier–breaking” SSSP blends BF-style bulk relaxations with frontier shrinking to converge near-linearly, avoiding heavy sorting while thousands of tracks and intercept windows appear or vanish each second.
Run the new SSSP to label each node with minimum “risk-to-asset” or “cost-to-intercept”. Backtrack shortest-cost paths to list viable intercept windows per track. Solve a min-cost assignment/flow over these candidates, using the SSSP labels as potentials, honoring ammo, thermal, and comms limits. When the graph changes—new tracks, spoofed targets, or link loss—apply incremental BF-style relaxations instead of full re-sorting. Roll the horizon forward in MPC fashion; re-use labels and partially relax to keep latency low.
4) Where Each Algorithm Fits
BF-style relaxations handle frequent reweights from EW effects or decoys and tolerate non-“nice” constraints. Dijkstra remains useful for stable local subproblems with fixed, non-negative costs (e.g., internal base logistics). The near-linear SSSP is the main engine for global deconfliction at swarm scale, where priority-queue sorting would choke.
5) Key Design Choices (Abstract, Not Tactical)
Cost shaping: encode asset criticality, blue-force exposure, and comms risk in edge weights; avoid negative cycles. Time expansion: keep coarse grids globally and refine adaptively near defended assets. Resilience: with jammed/noisy inputs, prefer batch relaxations and bounded-subgraph updates over global reorders. Scalability: shard by sector/altitude band; run SSSP per shard and stitch with lightweight inter-shard edges.
6) Outputs That Matter
Sets of feasible intercept windows per drone with confidence estimates, an assignment plan minimizing expected loss under practical limits, and sensitivity views showing how plans shift if a battery is denied or a track proves to be a decoy.
Bottom Line
Treat counter-swarm defense as repeated shortest-path labeling on a time-expanded, directed graph. Use BF-style relaxations for rapid, incremental updates, avoid global sorting overhead, and exploit near-linear SSSP to keep pace with swarm-scale dynamics—without delving into weapon-specific or targeting details.
This Python script is an educational, non-operational simulator that frames
counter-swarm planning as a time-expanded directed graph. It uses synthetic data to
explore how classic and modern single-source shortest-path (SSSP) algorithms can label low-cost
engagement opportunities without providing tactical or weapon-specific guidance.
The program prints a human-readable plan like
“Track 03 → Battery 1 at t=24” for selected matches,
plus a JSON summary: number of nodes/edges, solver time (ms), chosen intercepts, and total label cost.
Ethical / Scope Note: This is a toy simulator for academic exploration,
based entirely on synthetic data. It intentionally avoids weapon specifics, targeting detail,
or real-world tactics.
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Counter-swarm graph pipeline (educational demo)
-----------------------------------------------
Implements the abstract pipeline from the blog post:
- Time-expanded directed graph over horizon [0..T]
- SSSP variants: Bellman–Ford, Dijkstra, Delta-Stepping (bucketed near-linear)
- Backtrack to enumerate feasible intercept windows
- Min-cost assignment with ammo/thermal/comm limits
Ethical/Scope note: This is a toy simulator for academic exploration only.
It avoids weapon-specific or tactical guidance and uses synthetic data.
Source framing: https://rkhouja.blogspot.com/2025/08/countering-drone-swarms-with-graph.html
"""
from __future__ import annotations
import math, heapq, random, itertools, collections, time
from dataclasses import dataclass, field
from typing import Dict, Tuple, List, Optional, Iterable, Set
try:
import numpy as np
except Exception:
np = None # Optional; code will still run
# -----------------------------
# Domain model (synthetic)
# -----------------------------
@dataclass(frozen=True)
class TrackID:
k: int
@dataclass(frozen=True)
class BatteryID:
b: int
@dataclass
class Scenario:
"""Synthetic scenario generator."""
n_tracks: int
n_batteries: int
area: Tuple[float, float] = (40.0, 40.0) # km (toy)
vmax_drone: float = 0.25 # km/s (900 km/h ~ 0.25 km/s)
vmax_effector: float = 0.5 # km/s (toy)
kill_prob: float = 0.65 # baseline Pk
T: int = 60 # seconds horizon
dt: int = 3 # discretization step (s)
def generate(self, seed: int = 7):
rng = random.Random(seed)
W, H = self.area
# Random start and goal for drones; batteries fixed near bottom
tracks = {}
for k in range(self.n_tracks):
x0, y0 = rng.uniform(0, W), rng.uniform(H*0.5, H) # spawn upper half
gx, gy = rng.uniform(0, W), rng.uniform(0, H*0.2) # assets near bottom
tracks[TrackID(k)] = ((x0, y0), (gx, gy))
batteries = {}
for b in range(self.n_batteries):
x, y = (W*(b+1)/(self.n_batteries+1), rng.uniform(0, H*0.25))
batteries[BatteryID(b)] = (x, y)
return tracks, batteries
# -----------------------------
# Time-expanded graph
# -----------------------------
@dataclass
class Node:
"""Node in time-expanded graph."""
t: int # integer time index 0..T/dt
kind: str # 'track', 'asset', 'battery', 'intercept'
ref: Tuple # (TrackID) OR (BatteryID) OR composite
@dataclass
class Edge:
u: int
v: int
cost: float
@dataclass
class TimeExpandedGraph:
nodes: List[Node] = field(default_factory=list)
edges: List[Edge] = field(default_factory=list)
out_adj: List[List[int]] = field(default_factory=list) # edge indices
in_adj: List[List[int]] = field(default_factory=list)
def add_node(self, n: Node) -> int:
idx = len(self.nodes)
self.nodes.append(n)
self.out_adj.append([])
self.in_adj.append([])
return idx
def add_edge(self, u: int, v: int, cost: float):
eid = len(self.edges)
self.edges.append(Edge(u, v, cost))
self.out_adj[u].append(eid)
self.in_adj[v].append(eid)
# -----------------------------
# Cost shaping (abstract)
# -----------------------------
@dataclass
class CostModel:
asset_criticality: float = 10.0
time_to_impact_weight: float = 2.0
pk_weight: float = -4.0 # lowering cost if Pk is higher
collateral_penalty: float = 1.0
comms_latency_penalty: float = 0.2
reload_penalty: float = 0.4
thermal_penalty: float = 0.3
jam_risk_penalty: float = 0.5
def edge_cost_track_motion(self, dtime: float, dist_to_asset: float) -> float:
# Encourage shorter TTI by penalizing being far from asset as time advances
return self.time_to_impact_weight * (dist_to_asset / max(dtime, 1e-3))
def edge_cost_intercept(self, pk: float, collateral: float, comms: float,
reload: float, thermal: float, jam_risk: float) -> float:
return (self.pk_weight * pk +
self.collateral_penalty * collateral +
self.comms_latency_penalty * comms +
self.reload_penalty * reload +
self.thermal_penalty * thermal +
self.jam_risk_penalty * jam_risk)
def edge_cost_asset_hit(self, criticality: float) -> float:
return self.asset_criticality * criticality
# -----------------------------
# Graph builder
# -----------------------------
class GraphBuilder:
def __init__(self, scenario: Scenario, cost_model: CostModel):
self.sc = scenario
self.cm = cost_model
def _drone_pos(self, p0, p1, alpha):
# Linear motion to goal (toy)
x = p0[0] + (p1[0]-p0[0]) * alpha
y = p0[1] + (p1[1]-p0[1]) * alpha
return (x, y)
def _dist(self, a, b):
return math.hypot(a[0]-b[0], a[1]-b[1])
def build(self, seed: int = 0) -> Tuple[TimeExpandedGraph, Dict]:
rng = random.Random(seed)
tracks, batteries = self.sc.generate(seed=seed)
T = self.sc.T
dt = self.sc.dt
steps = T // dt
g = TimeExpandedGraph()
idx = {}
# Create nodes
for t in range(steps+1):
alpha = t / float(steps)
for k, (p0, p1) in tracks.items():
pos = self._drone_pos(p0, p1, alpha)
idx_key = ('track', k.k, t)
idx[idx_key] = g.add_node(Node(t=t, kind='track', ref=(k, pos)))
# assets (just one synthetic protected line near y=0)
idx[('asset', t)] = g.add_node(Node(t=t, kind='asset', ref=('asset_line', 0.0)))
for b_id, bpos in batteries.items():
idx_key = ('battery', b_id.b, t)
idx[idx_key] = g.add_node(Node(t=t, kind='battery', ref=(b_id, bpos)))
# Edges: track motion across time, cost increases as they approach asset
for t in range(steps):
t2 = t + 1
for k, (p0, p1) in tracks.items():
a1 = t / float(steps); a2 = t2 / float(steps)
pos1 = self._drone_pos(p0, p1, a1)
pos2 = self._drone_pos(p0, p1, a2)
d_to_asset = pos2[1] # distance to y=0 boundary (toy)
u = idx[('track', k.k, t)]
v = idx[('track', k.k, t2)]
cost = self.cm.edge_cost_track_motion(self.sc.dt, d_to_asset)
g.add_edge(u, v, cost)
# Edges: intercept windows (battery -> track at same time)
for t in range(steps+1):
for b_id, bpos in batteries.items():
bnode = idx[('battery', b_id.b, t)]
for k, (p0, p1) in tracks.items():
alpha = t / float(steps)
kpos = self._drone_pos(p0, p1, alpha)
dist = self._dist(bpos, kpos)
# Feasible if inside effector kinematics window (toy)
feasible = dist <= self.sc.vmax_effector * self.sc.dt * max(1, t+1)
if not feasible:
continue
# Abstract costs
pk = self._pk_from_distance(dist)
collateral = 0.1 if kpos[1] > 5 else 0.3
comms = 0.2 + 0.01 * t
reload = 0.4 if (t % 5 == 0) else 0.1
thermal = 0.2 + 0.05 * (t % 4)
jam_risk = 0.15 + 0.02 * (t % 3)
cost = self.cm.edge_cost_intercept(pk, collateral, comms, reload, thermal, jam_risk)
g.add_edge(bnode, idx[('track', k.k, t)], cost)
# Edges: track -> asset hit at final layer (penalize)
for k in tracks.keys():
v = idx[('track', k.k, steps)]
u = idx[('asset', steps)]
cost = self.cm.edge_cost_asset_hit(criticality=1.0)
g.add_edge(v, u, cost)
aux = dict(idx=idx, steps=steps, tracks=tracks, batteries=batteries)
return g, aux
def _pk_from_distance(self, d):
# Toy Pk model: monotonically decays with distance
return max(0.0, 1.1 * math.exp(-0.12 * d) - 0.1)
# -----------------------------
# SSSP solvers
# -----------------------------
INF = 1e30
class BellmanFord:
@staticmethod
def solve(g: TimeExpandedGraph, source_nodes: Iterable[int]) -> Tuple[List[float], List[int]]:
n = len(g.nodes)
dist = [INF]*n
parent = [-1]*n
for s in source_nodes:
dist[s] = 0.0
# Relax E edges up to V-1 times
for _ in range(n-1):
changed = False
for eid, e in enumerate(g.edges):
if dist[e.u] + e.cost < dist[e.v]:
dist[e.v] = dist[e.u] + e.cost
parent[e.v] = e.u
changed = True
if not changed:
break
# Negative cycles not expected in this toy (we avoid them in cost shaping)
return dist, parent
class Dijkstra:
@staticmethod
def solve(g: TimeExpandedGraph, source_nodes: Iterable[int]) -> Tuple[List[float], List[int]]:
n = len(g.nodes)
dist = [INF]*n
parent = [-1]*n
pq = []
for s in source_nodes:
dist[s] = 0.0
heapq.heappush(pq, (0.0, s))
while pq:
d,u = heapq.heappop(pq)
if d != dist[u]:
continue
for eid in g.out_adj[u]:
e = g.edges[eid]
nd = d + e.cost
if nd < dist[e.v]:
dist[e.v] = nd
parent[e.v] = u
heapq.heappush(pq, (nd, e.v))
return dist, parent
class DeltaStepping:
"""
Bucketed near-linear SSSP for non-negative weights.
Good when many edges have small bounded weights and the frontier can be
relaxed in bulk (avoids global sorting bottleneck).
"""
@staticmethod
def solve(g: TimeExpandedGraph, source_nodes: Iterable[int], delta: float = 1.0) -> Tuple[List[float], List[int]]:
n = len(g.nodes)
dist = [INF]*n
parent = [-1]*n
B: Dict[int, Set[int]] = collections.defaultdict(set)
def bucket_index(x: float) -> int:
return int(x // delta)
for s in source_nodes:
dist[s] = 0.0
B[0].add(s)
i = 0
while True:
# Find next non-empty bucket
while i in B and not B[i]:
i += 1
if i not in B:
break
S = set()
R = set(B[i]) # requests
# Light-edge relaxations
while R:
S |= R
R2 = set()
for u in list(R):
for eid in g.out_adj[u]:
e = g.edges[eid]
w = e.cost
nd = dist[u] + w
if nd < dist[e.v] and w <= delta:
old = dist[e.v]
dist[e.v] = nd
parent[e.v] = u
if old < INF:
B[bucket_index(old)].discard(e.v)
R2.add(e.v)
R = R2
# Heavy-edge relaxations
for u in list(S):
for eid in g.out_adj[u]:
e = g.edges[eid]
w = e.cost
if w > delta:
nd = dist[u] + w
if nd < dist[e.v]:
old = dist[e.v]
dist[e.v] = nd
parent[e.v] = u
if old < INF:
B[bucket_index(old)].discard(e.v)
B[bucket_index(nd)].add(e.v)
B[i].clear()
return dist, parent
# -----------------------------
# Backtracking intercept windows
# -----------------------------
def backtrack_path(parent: List[int], target: int) -> List[int]:
path = []
u = target
while u != -1:
path.append(u)
u = parent[u]
path.reverse()
return path
@dataclass
class InterceptCandidate:
track: TrackID
battery: BatteryID
time_index: int
node_idx: int
label_cost: float
def enumerate_intercepts(g: TimeExpandedGraph, dist: List[float], aux: Dict,
top_k: int = 3) -> Dict[TrackID, List[InterceptCandidate]]:
"""Pick top-K intercept windows per track (lowest labeled cost near asset)."""
idx = aux['idx']
steps = aux['steps']
tracks: Dict[TrackID, Tuple[Tuple[float,float], Tuple[float,float]]] = aux['tracks']
batteries: Dict[BatteryID, Tuple[float,float]] = aux['batteries']
results = {}
for k in tracks.keys():
cands = []
for t in range(steps+1):
tr_node = idx[('track', k.k, t)]
# Find any incoming edges from batteries at same t
for eid in g.in_adj[tr_node]:
e = g.edges[eid]
u_node = g.nodes[e.u]
if u_node.kind != 'battery' or u_node.t != t:
continue
b_id, _ = u_node.ref
cands.append(InterceptCandidate(track=k, battery=b_id, time_index=t,
node_idx=tr_node, label_cost=dist[tr_node]))
cands.sort(key=lambda c: c.label_cost)
results[k] = cands[:top_k]
return results
# -----------------------------
# Min-cost assignment (bipartite)
# -----------------------------
@dataclass
class AssignmentLimits:
ammo_per_battery: int = 3
thermal_cooldown: int = 2 # minimal time distance between shots per battery
comms_slots_per_t: int = 999 # unlimited in toy
def min_cost_assign(intercepts: Dict[TrackID, List[InterceptCandidate]],
limits: AssignmentLimits) -> Dict[TrackID, Optional[InterceptCandidate]]:
"""
Greedy + tie-breaker matching:
- Iterate tracks by best available label
- Enforce ammo and per-battery cooldown
This is deliberately simple, readable, and deterministic.
"""
# Flatten candidates
flat = []
for k, lst in intercepts.items():
for c in lst:
flat.append((c.label_cost, k, c))
flat.sort(key=lambda x: x[0])
# State
ammo_left = collections.Counter()
last_shot_t = {}
chosen: Dict[TrackID, Optional[InterceptCandidate]] = {k: None for k in intercepts.keys()}
for _, k, c in flat:
if chosen[k] is not None:
continue
b = c.battery
if ammo_left[b] >= limits.ammo_per_battery:
continue
t_prev = last_shot_t.get(b, -10**9)
if c.time_index - t_prev < limits.thermal_cooldown:
continue
chosen[k] = c
ammo_left[b] += 1
last_shot_t[b] = c.time_index
return chosen
# -----------------------------
# Pipeline runner
# -----------------------------
def run_pipeline(sssp: str = "delta", seed: int = 0):
sc = Scenario(n_tracks=12, n_batteries=4, T=60, dt=3)
cm = CostModel()
gb = GraphBuilder(sc, cm)
g, aux = gb.build(seed=seed)
# Select source nodes (batteries at t=0)
sources = []
for b_id in aux['batteries'].keys():
sources.append(aux['idx'][('battery', b_id.b, 0)])
t0 = time.time()
if sssp == "bf":
dist, parent = BellmanFord.solve(g, sources)
elif sssp == "dij":
dist, parent = Dijkstra.solve(g, sources)
else:
dist, parent = DeltaStepping.solve(g, sources, delta=1.0)
t1 = time.time()
# Enumerate intercept windows & assign
intercepts = enumerate_intercepts(g, dist, aux, top_k=3)
plan = min_cost_assign(intercepts, AssignmentLimits(ammo_per_battery=3, thermal_cooldown=2))
# Summarize
total_cost = 0.0
taken = 0
lines = []
for k, sel in sorted(plan.items(), key=lambda kv: kv[0].k):
if sel is None:
lines.append(f"Track {k.k:02d}: NO INTERCEPT SELECTED")
else:
total_cost += sel.label_cost
taken += 1
lines.append(f"Track {k.k:02d}: Battery {sel.battery.b} at t={sel.time_index} "
f"(label={sel.label_cost:.2f})")
summary = {
"sssp": sssp,
"nodes": len(g.nodes),
"edges": len(g.edges),
"solvetime_ms": round(1000*(t1-t0), 2),
"intercepts_selected": taken,
"total_label_cost": round(total_cost, 3)
}
return summary, lines
# -----------------------------
# CLI
# -----------------------------
def main():
import argparse, json
ap = argparse.ArgumentParser(description="Counter-swarm graph pipeline (toy).")
ap.add_argument("--algo", choices=["bf", "dij", "delta"], default="delta",
help="SSSP algorithm: Bellman–Ford (bf), Dijkstra (dij), Delta-Stepping (delta).")
ap.add_argument("--seed", type=int, default=0)
args = ap.parse_args()
summary, lines = run_pipeline(sssp=args.algo, seed=args.seed)
print("# Plan (toy, abstract):")
for ln in lines:
print(ln)
print("\n# Summary:")
print(json.dumps(summary, indent=2))
if __name__ == "__main__":
main()
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