Modified Greedy Routing

• Modified Greedy Routing is a set of algorithmic strategies that overcome classical greedy forwarding limitations by incorporating local backtracking, void-avoidance, and dynamic path selection.
• It employs techniques such as sector extrapolation, energy-aware candidate scoring, and machine-learned forwarding rules to improve delivery success and reduce route stretch.
• These approaches are applied in networks ranging from wireless sensor and mesh networks to complex graphs, demonstrating enhanced packet delivery ratios and energy efficiency.

Modified Greedy Routing encompasses algorithmic strategies that generalize, enhance, or otherwise adapt classical greedy forwarding in networks to achieve improved robustness, efficiency, and applicability under practical constraints of topology, mobility, energy, or user behavior. Central themes across research include topology-agnosticity, energy-awareness, dynamic adaptation to voids or obstacles, multipath load balancing, combinatorial coordinate systems, machine-learned forwarding rules, and analytical guarantees on delivery success, path stretch, and computational overhead. These modifications are motivated by the limitations of baseline greedy forwarding in the presence of holes, non-planarity, node failures, or lack of global knowledge, and are evaluated in scenarios from wireless sensor networks and mesh networks to social graphs, planar triangulations, and internet-scale random graphs.

1. Classical Greedy Forwarding and Its Limitations

Baseline greedy routing is characterized by per-hop decisions that forward a packet to the one-hop neighbor minimizing a metric such as Euclidean or graph-theoretic distance to the destination. In planar networks, GPSR (Greedy Perimeter Stateless Routing) is the canonical protocol, relying on local neighbor coordinates and switching to perimeter (face) routing when greedy progress fails. However, multiple limitations emerge:

• Local Minimum Problem: Greedy forwarding gets trapped at nodes with no neighbor closer to the destination, commonly at the border of holes or voids.
• Non-Planarity and Connectivity: Planarization required for face routing may be inapplicable or unreliable in arbitrary graphs, leading to dropped packets or excessive control overhead (0902.4157).
• Energy Inefficiency: Uniform traffic can rapidly deplete key nodes, reducing network lifetime in resource-constrained deployments (Medjiah et al., 2012).
• Mobility and Dynamic Topology: In highly mobile settings (e.g., UAV networks), static shortest-path setups become stale and costly, undermining reliability (Khaledi et al., 2018).
• Suboptimal Path Stretch and Load Distribution: Classic greedy may induce long detours or hotspot formation, hurting delay and energy metrics (Fei et al., 2015, Noghabi et al., 2012).

2. Void-Avoidance and Local Backtracking Strategies

To guarantee delivery or mitigate path stretch in the presence of voids, modified greedy routing incorporates local mechanisms to escape dead ends:

• Walking-back Forwarding and Backtracking: Upon detection of a dead-end (no closer neighbor), protocols such as AGEM and GRB engage in localized walking-back or backtracking, flooding “NO_PATH_TO_SINK” messages or returning packets hop-by-hop to previous transmitters until a viable forwarder is reached (Medjiah et al., 2012, Mahmood et al., 2018).
• Seen Table and Verification: GRB uses Seen Tables to record which neighbors have failed in forwarding for a given (Src, Dst) pair, avoiding repeated cycles and guaranteeing loop-freeness. Backtracking proceeds until all candidates are exhausted, maintaining low control overhead compared to face routing or full flooding.

Protocol	Void Handling Mechanism	Local State Maintained
AGEM	Walking-back delegation	Hole labels, candidate memorization
GRB	One-hop backtracking	Seen Table for tried/failure links

These strategies avoid the complexity and overhead of planarization and perimeter routing, guaranteeing high packet delivery ratios (PDR > 98% for GRB, compared to GPSR and AODV) and reducing delay and energy consumption (Mahmood et al., 2018).

3. Reactive Deflection and Sector Extrapolation

Modified greedy geographic routing can further exploit sector-based blocked-region identification and propagation:

• Blocked Sectors Representation: Nodes dynamically record directions (angular sectors) and distances where voids prevent progress, updating and merging these per-destination blocklists as packets encounter dead ends.
• Information Propagation: Sector data is distributed via HELLO messages with limited TTL, enabling each node to learn blocked directions within k-hop neighborhoods, reducing redundant retries and route-length stretch (0902.4157).
• Extrapolation and Optimized Next-Hop Selection: By constructing forbidden sectors and their boundaries around voids, packets are steered around perimeters with minimal route inflation, maintaining loop-freedom and localized control, even in non-planar graphs.

Simulation evidence demonstrates dramatic improvement over naive greedy routing in spontaneous mesh networks, reducing packet loss from >70% to <4% and containing route stretch within 10-20% of pure greedy (0902.4157).

4. Energy-Aware and Multipath Load-Balancing Variants

Energy-aware greedy routing extends baseline protocols by integrating node residual energy, radio consumption models, and load balancing heuristics:

• Candidate Scoring: AGEM computes a neighbor score $f(v)$ by subtracting per-hop transmission and reception energy from estimated residual energy, biasing towards energy-rich and nearer nodes (Medjiah et al., 2012).
• Empirical Load Distribution: By tracking per-source hop counts and adjusting candidate rank selection (prefer higher-scoring neighbors for packets that have traveled longer), AGEM achieves multipath spreading and uniform energy depletion, minimizing dead zones and maximizing network lifetime.
• Grid-based Hierarchical Greedy Chain Routing: PGC partitions the field into hexagonal cells, designating single Gateway nodes per cell with mask-based greedy selection. Combined with touch-aware “sink sliding” to avoid border congestion, PGC demonstrates 20-25% higher energy retention and doubled packet delivery under lossy conditions compared to LEACH (Noghabi et al., 2012).

Protocol	Energy Model	Load-Balancing Technique
AGEM	Residual – transmission	Empirical hop-count per source, compass
PGC	Mask ID + residual	Grid cell duty-cycling, sink movement

5. Combinatorial, Metric-Free, and Machine-Learned Greedy Routing

Recent work generalizes greedy routing to non-metric, combinatorial coordinate systems or data-driven forwarding policies:

• Metric-Free Routing in Planar Triangulations: Instead of geometric embeddings, succinct greedy routing assigns combinatorial coordinates using three total orders (Schnyder representation), partitioning neighbors into six sectors and enforcing monotonic progress in rank without reference to metric. This method is proven to guarantee delivery with $O(\log n)$ coordinate size, circumventing localization and floating-point error (Leone et al., 2015).
• Machine-Learned Policies: Knowledge-guided deep learning yields local forwarding rules such as Greedy Tensile, which optimally weights distance-to-destination and tensile node stretch. Symbolic interpretation reduces the DNN to two linear actions over neighbor features, nearly matching shortest-path stretch (1.04 vs. 1.10 for plain greedy) with 97% “success” rate within $\epsilon=0.05$ stretch (Chen et al., 8 Sep 2025). Theoretical guarantees (Pointwise Monotonicity, RankPreservation) ensure cross-graph generalization.

Policy	Input Features	Empirical Path Stretch	Success Rate (≤1+ε)
Plain Greedy	Distance-to-destination	1.10	88.5%
Greedy Tensile RL	Distance, Stretch	1.04	95.5%

6. Hybrid and Small-World Modifications for Algorithmic Scalability

Network models demonstrating small-world phenomena (Kleinberg, FG-graphs, GIRG) motivate augmentations that enable efficient greedy routing in large-scale graphs:

• Randomized Highway Augmentation: Fixed-growth graphs of dimension $\alpha$ are augmented with sparsely marked “highway” nodes, each with long-range contacts distributed with power-law bias $d(u,v)^{-\alpha}$. Greedy routing across local edges and highways yields $O(\log n)$ expected routing time for $\alpha>2$, outperforming lattice-restricted models, and empirical evaluation on U.S. state road networks confirms optimal clustering exponent $s\approx\alpha$ (Gila et al., 5 Feb 2025).
• GIRG and Hyperbolic Internet Routing: Geometric inhomogeneous random graphs combine location, vertex weight, and probabilistic connectivity. Greedy routing using a localized objective $w_v / (n \|\mathbf{x}_v-\mathbf{x}_t\|^d)$ is proven to deliver almost shortest paths of length $\Theta(\log\log n)$ with constant probability, but local patching (backtracking, plateau exploration) guarantees success w.p.$\to1$ in asymptotically tight hops (Bringmann et al., 2016).

7. Advanced Heuristics: Intermediate Targets, Navigational Memory, and Structural Insights

Protocols have incorporated user experience and memory to further optimize routing for real deployments:

• Intermediate Target Geographic Routing (ITGR): Shaded regions “behind” holes are defined via half-plane tests, with landmark nodes recorded upon perimeter-mode exits. These caches allow sources to route via intermediate targets, systematically avoiding known detours and reducing average path length by 17–19% and worst-case detour lengths by up to 80% relative to GPSR (Fei et al., 2015).
• Greedy Navigators with Memory and Braess's Paradox: Agents navigating spatial networks with greedy bearing and memory-based backtracking exhibit counterintuitive effects, such as improved path efficiency upon removal of “attractor” edges, reminiscent of Braess’s paradox. Empirical analysis on urban roads and railways shows greedy navigability $\nu$ is city-specific and not readily predicted by standard centralities, revealing rich structural signatures missed by classical metrics (Lee et al., 2011).

• AGEM: Adaptive Greedy-Compass Energy-aware Multipath Routing Protocol (Medjiah et al., 2012)
• Modified Greedy Geographic Routing with Reactive Deflection (0902.4157)
• Greedy Routing Protocol with Backtracking (GRB) (Mahmood et al., 2018)
• Fast Geographic Routing in Fixed-Growth Graphs (Gila et al., 5 Feb 2025)
• Knowledge-Guided Machine Learning for Stabilizing Near-Shortest Path Routing (Chen et al., 8 Sep 2025)
• Improved Routing with Intermediate Target Geographic Routing (Fei et al., 2015)
• Succinct Greedy Routing without Metric on Planar Triangulations (Leone et al., 2015)
• Exploring Maps with Greedy Navigators (Lee et al., 2011)
• Greedy Routing and the Algorithmic Small-World Phenomenon (Bringmann et al., 2016)
• On Greedy Routing in Dynamic UAV Networks (Khaledi et al., 2018)
• Implementing a Greedy Chain Routing Technique with Spread Spectrum (Noghabi et al., 2012)

Modified greedy routing thus comprises a wide arsenal of localized, efficient, theoretically grounded strategies critical for the scalability, robustness, and adaptability of modern networked systems across application domains.