Comm-Aware Mode Distribution Planning

• The paper demonstrates that communication-aware mode distribution planning integrates communication constraints into optimization formulations to co-design cyber-physical systems.
• It employs mathematical models such as Laplacian quadratic costs and SINR constraints to jointly optimize mobility, relay placement, and energy consumption.
• Key implications include improved resource allocation in diverse systems like mobile networks, D2D communications, and multi-robot teams through tailored optimization and decomposition methods.

Searching arXiv for the cited papers to ground the article. Communication-aware mode distribution planning denotes a class of optimization problems in which communication constraints, communication cost, or communication utility directly shape how roles, resources, trajectories, or abstractions are distributed across agents, links, channels, or spatial regions. Across the literature, the same underlying question appears under different names: mobile relays are positioned to trade mobility energy against communication energy; D2D pairs select between direct and cellular relaying modes; robot teams distribute communication-support and task-execution roles; virtual networks are embedded on bandwidth-rich substrate paths; grid reconfiguration is conditioned on control-center reachability; and map abstractions or ISAC beam powers are allocated according to their effect on downstream planning performance (Jaleel et al., 2016, Wang et al., 2016, Liu et al., 2017, Mikkelsen et al., 2024, Psomiadis et al., 13 Mar 2025, Jin et al., 27 Oct 2025).

1. Conceptual scope and representative problem classes

A common abstraction emerges when the decision variable is not only where to move or which channel to use, but also which communication-dependent operating mode should be assigned where and when. In the mobile-relay setting, the “mode” is implicit in the magnitude of motion and in the resulting relay geometry; in D2D systems it is explicit as D2D mode versus cellular mode; in resilient distribution systems it appears as normal, islanded, or post-disaster reconfiguration conditioned on communication reachability; in map compression it is the choice of abstraction template; and in ISAC it is the spatial distribution of sensing/communication power over obstacle-directed beams (Jaleel et al., 2016, Wang et al., 2016, Byeon et al., 2018, Psomiadis et al., 13 Mar 2025, Jin et al., 27 Oct 2025).

Domain	Mode or role being distributed	Representative paper
Mobile relay networks	movement, relay placement, idle/relay interpretation	(Jaleel et al., 2016)
Cellular/D2D systems	D2D mode, cellular mode, channel reuse	(Wang et al., 2016, Librino et al., 28 Feb 2025)
IoV virtualized networks	bandwidth-aware mapping and path choice	(Zhang et al., 2022)
Distribution grids	controllable islanding and communication-reachable operation	(Byeon et al., 2018)
Multi-robot planning	inspection vs support/relay behavior, communication-preserving motion	(Mikkelsen et al., 2024, Mikkelsen et al., 2024, Marchukov et al., 24 Mar 2025)
Online navigation and ISAC	compression template or beam-power allocation	(Psomiadis et al., 13 Mar 2025, Jin et al., 27 Oct 2025)

This breadth is not accidental. In each case, communication enters as a scarce or state-dependent resource whose availability determines feasible operating patterns. The literature therefore treats mode distribution as a cyber-physical co-design problem rather than a purely networking or purely control problem. Formal-methods variants make this explicit by encoding motion objectives in STL and communication objectives in STREL or SpaTeL, so that trajectory synthesis and communication-structure synthesis are solved together rather than sequentially (Liu et al., 2018, Liu et al., 2017).

2. Optimization primitives and mathematical formulations

The most common formulation is a constrained optimization in which communication terms appear either in the objective, in feasibility constraints, or in both. In energy-aware coordinated mobility, the stage cost is

$$g({\bf z}_k,{\bf u}_k)= {\bf z}_k^\top Q\,{\bf z}_k + {\bf u}_k^\top R\,{\bf u}_k,$$

with $Q=\frac{\kappa_C}{2}(L\otimes I_2)$ encoding communication cost and $R=\kappa_M I_{2N}$ encoding mobility cost; the resulting infinite-horizon discounted problem is a linear-quadratic dynamic program whose optimal value function is quadratic, $J^*({\bf z})={\bf z}^\top K{\bf z}$ (Jaleel et al., 2016). In D2D systems, the analogous mode variables are discrete: $\rho_{i,j}$ indicates whether channel $i$ is assigned to link $j$, and $x_j$ indicates whether a D2D pair uses cellular mode or D2D mode; the objective is a weighted sum-rate under SINR constraints for both cellular and D2D links (Wang et al., 2016).

Several papers make the communication-aware structure explicit through bilevel or two-stage formulations. The ORDPDC model uses a first-stage investment vector

$$w = \bigl( x_{E_x^n}, t_{E_t^n}, h_{E_h}, u_{U^n} \bigr) \in \{0,1\}^m$$

for line/link construction, switch installation, hardening, and DG placement, and second-stage scenario-specific recourse that must satisfy power-flow, radiality, communication-reachability, and resiliency constraints under each disaster scenario (Byeon et al., 2018). PISAC uses a bilevel power allocation and motion planning problem in which the outer layer minimizes

$$C_0(\{\mathbf{s}_t^E,\mathbf{u}_t^E\})=\sum_{t=0}^H \big\|\mathbf{s}_t^E-\mathbf{s}_t^\diamond\big\|_2^2$$

subject to uncertainty-aware safety constraints, while the inner layer allocates ISAC beam powers $Q=\frac{\kappa_C}{2}(L\otimes I_2)$0 under a sum-rate constraint and a sum-power constraint (Jin et al., 27 Oct 2025).

A distinct but related formulation appears in online path-planning with compressed maps. There, the mode variable is a template $Q=\frac{\kappa_C}{2}(L\otimes I_2)$1, selected by the encoder according to

$Q=\frac{\kappa_C}{2}(L\otimes I_2)$2

with $Q=\frac{\kappa_C}{2}(L\otimes I_2)$3 in the simulations and bit cost $Q=\frac{\kappa_C}{2}(L\otimes I_2)$4 (Psomiadis et al., 13 Mar 2025). This suggests a general interpretation in which a mode is any communication action whose effect can be propagated through a belief update and then evaluated by its effect on task cost.

3. Communication models, QoS metrics, and state representations

The literature employs several non-equivalent notions of “communication-aware,” each tailored to the target domain. In relay-motion problems, communication cost is spatial and graph-theoretic: with a line graph $Q=\frac{\kappa_C}{2}(L\otimes I_2)$5, the communication cost is a Laplacian quadratic

$Q=\frac{\kappa_C}{2}(L\otimes I_2)$6

so shorter hops reduce communication energy but usually require motion (Jaleel et al., 2016). In multi-robot connectivity-constrained planning, communication quality is the Fiedler value $Q=\frac{\kappa_C}{2}(L\otimes I_2)$7 of the weighted graph Laplacian, with edge weights

$Q=\frac{\kappa_C}{2}(L\otimes I_2)$8

and the hard requirement $Q=\frac{\kappa_C}{2}(L\otimes I_2)$9 or $R=\kappa_M I_{2N}$0 (Mikkelsen et al., 2024, Mikkelsen et al., 2024).

In D2D and IoV settings, the communication model is interference- and bandwidth-centric. QoS-aware D2D planning uses a unified SINR expression

$R=\kappa_M I_{2N}$1

whose numerator depends on the selected mode $R=\kappa_M I_{2N}$2 and whose denominator aggregates interference from cellular-mode and D2D-mode co-channel users (Wang et al., 2016). The hybrid D2D framework instead builds local power-control decisions around the functions

$R=\kappa_M I_{2N}$3

which quantify D2D decoding success and CUE blockage risk (Librino et al., 28 Feb 2025). BA-VNE is “bandwidth aware” in a more literal sense: candidate substrate links are pre-filtered by

$R=\kappa_M I_{2N}$4

and the resulting virtual network embedding optimizes mapping cost, VNR acceptance rate, and link utilization in a multi-domain architecture with local and global controllers (Zhang et al., 2022).

Spatial communication representations can also be coarse and symbolic. In RSS-based deployment planning, a point is in coverage when $R=\kappa_M I_{2N}$5, with path loss

$R=\kappa_M I_{2N}$6

coverage sets $R=\kappa_M I_{2N}$7, and a goal-connectivity graph $R=\kappa_M I_{2N}$8 defined by pairwise RSS thresholds (Marchukov et al., 24 Mar 2025). In SpaTeL-based planning, the environment is encoded as a $R=\kappa_M I_{2N}$9 matrix $J^*({\bf z})={\bf z}^\top K{\bf z}$0, embedded as a quad-tree; each cell’s valuation $J^*({\bf z})={\bf z}^\top K{\bf z}$1 is interpreted as a capacity-like communication/safety label, and formulas constrain where and how many agents may occupy regions over time (Liu et al., 2017). STREL-based planning instead reasons over graph routes and bounded hops through formulas such as

$J^*({\bf z})={\bf z}^\top K{\bf z}$2

which require every robot to reach a base within at most two hops while disallowing relay–relay adjacency (Liu et al., 2018).

A further variant appears in planning-oriented ISAC, where communication and sensing are tied through CRB-derived uncertainty. The covariance of obstacle state estimate $J^*({\bf z})={\bf z}^\top K{\bf z}$3 is

$J^*({\bf z})={\bf z}^\top K{\bf z}$4

so higher beam power $J^*({\bf z})={\bf z}^\top K{\bf z}$5 reduces uncertainty and hence the inflated obstacle dimensions

$J^*({\bf z})={\bf z}^\top K{\bf z}$6

which directly determines the safe navigable corridor (Jin et al., 27 Oct 2025).

4. Algorithmic architectures

Exact centralized optimization is rare outside small instances. The literature instead organizes around a spectrum from exact but expensive methods to sparse, local, or hierarchical approximations. In coordinated mobility, the exact dynamic-programming/LQR solution is centralized because the Riccati solution $J^*({\bf z})={\bf z}^\top K{\bf z}$7 has non-zero entries coupling every agent to every other agent; this motivates EAP I, EAP II, and EAP III, which replace the global value function with sparse approximations $J^*({\bf z})={\bf z}^\top K{\bf z}$8 that respect graph sparsity, yielding distributed or decentralized policies (Jaleel et al., 2016). EAP III, for example, reduces to a consensus-type update

$J^*({\bf z})={\bf z}^\top K{\bf z}$9

For QoS-aware D2D mode/channel planning, the exact benchmark is a dynamic program over states $\rho_{i,j}$0 that recursively assigns uplink and downlink channels while checking SINR feasibility; the practical alternative is a bipartite-graph-based greedy algorithm that first assigns channels to cellular links via Kuhn-Munkres matching and then greedily inserts D2D links and their modes according to incremental channel-value gains (Wang et al., 2016). The hybrid D2D paper moves the fast-timescale component entirely to the edge: a centralized epoch-level pairing and mode choice is combined with a per-slot distributed power allocation rule

$\rho_{i,j}$1

whose optimal policy partitions the $\rho_{i,j}$2 plane into at least 2 and at most $\rho_{i,j}$3 continuous regions $\rho_{i,j}$4 (Librino et al., 28 Feb 2025).

In graph-constrained or infrastructure-constrained settings, decomposition is typically scenario-based or hierarchy-based. ORDPDC is solved by an exact branch-and-price algorithm in which each scenario-specific pricing problem generates a feasible second-stage configuration consistent with dual prices from a restricted master problem; the acceleration mechanisms include pessimistic reduced cost, an optimality cut, and a lexicographic objective (Byeon et al., 2018). BA-VNE constructs a reduced global candidate-node network from locally aggregated multi-domain information, then uses PSO-based pre-mapping over this reduced graph; local controllers perform candidate-node selection and link aggregation, while the global controller handles inter-domain embedding (Zhang et al., 2022).

Robot planning papers favor distributed convexification or logic compilation. The Fiedler-value trajectory planners linearize the connectivity constraint through a first-order approximation

$\rho_{i,j}$5

and linearize collision avoidance through buffered Voronoi partitions, yielding linearly constrained quadratic programs over MPC horizons (Mikkelsen et al., 2024). The ADMM-based extension interprets $\rho_{i,j}$6 as a communication budget, splits it equally, and then allows trading through variables $\rho_{i,j}$7 constrained by $\rho_{i,j}$8, so that robots can buy or sell connectivity margin while solving only local subproblems (Mikkelsen et al., 2024). Formal-methods approaches compile STL, STREL, or SpaTeL formulas into MILP constraints and solve them within distributed MPC loops; the high-level route may be supplied by Delaunay-triangulation waypoints, while the low-level controller ensures logical satisfaction and communication robustness (Liu et al., 2018, Liu et al., 2017).

Path-planning and deployment papers emphasize graph search and geometric decomposition. The UAV surveillance work embeds communication as a constraint into a Theta*-style any-angle search with angle, leg-length, and coverage-hole restrictions; communication holes are constrained by

$\rho_{i,j}$9

for each zero-coverage segment (Sharma et al., 2017). The indoor deployment work combines CA-FMM, DP-FMM, and DPA-FMM: Fast Marching uses a modified speed field $i$0 to prefer connected areas, the deployment planner computes connectivity trees and relay destinations, and a clustering plus Hungarian-assignment plus small TSP routine allocates multi-goal tours and relay roles (Marchukov et al., 24 Mar 2025). In map-compression planning, exhaustive search over a finite template set $i$1 remains feasible because the decoder is a linear-Gaussian Kalman-style update with projection, not a growing quadratic program (Psomiadis et al., 13 Mar 2025).

5. Guarantees, operating trade-offs, and empirical behavior

Several papers provide explicit performance guarantees. In approximate dynamic programming for coordinated mobility, if $i$2 approximates the optimal value function, then the greedy policy $i$3 satisfies

$i$4

with $i$5; for the reported simulation, total costs were $i$6 for the optimal policy, $i$7 for EAP I, $i$8 for EAP II, and $i$9 for EAP III, showing the penalty induced by origin bias in EAP I and the near-optimality of the more communication-aware approximations (Jaleel et al., 2016).

The benefit of explicit bandwidth-aware or communication-aware distribution is similarly visible in networking results. In BA-VNE, BA-VNE and MC-VNM stabilize around ~60% VNR acceptance while VNE-PSO and LID-VNE drop to around ~30%; BA-VNE’s average embedding delay stays below 500 while MC-VNM exceeds 850 and LID-VNE and VNE-PSO exceed 600; and BA-VNE selects links with higher average bandwidth than both the domain average and MP-VNE because of the above-average-bandwidth filtering rule (Zhang et al., 2022). In D2D/cellular planning, allowing each channel to be accessed by multiple D2D links gives higher weighted sum-rate than restricting to at most one D2D link per channel, and the bipartite-graph-based greedy algorithm remains close to the optimal DP benchmark in the reported simulations (Wang et al., 2016). The hybrid D2D framework reports that, at $j$0 and $j$1 dB, CMP improves total throughput by about 63% over GEO; with $j$2 power levels and $j$3, $j$4 pkt/slot, about 10% above the single-power-level CMP and about four times GEO in that setting (Librino et al., 28 Feb 2025).

Infrastructure and planning papers make the same point with different metrics. ORDPDC shows that communication topology changes investment plans materially: in the rural network at 3% damage, the objective is 1914.99 for $j$5, 1948.09 for $j$6, and 2095.74 for $j$7, with the low-control-center case shifting toward more hardening and fewer DGs (Byeon et al., 2018). In online map compression, the proposed abstraction-selection method reduces communicated bits by about 98.4% on the Mars case, with $j$8 against $j$9, while maintaining comparable path cost; on the Earth case it achieves $x_j$0 with $x_j$1 versus $x_j$2 (Psomiadis et al., 13 Mar 2025).

Multi-robot and path-planning studies emphasize computational tractability and emergent role allocation. The approximate Fiedler-constrained MPC reduces per-iteration runtime from a mean of about 3823 ms and median about 3963 ms for the original nonlinear formulation to a mean about 3.27 ms and median about 2.88 ms for the approximated QP, while producing trajectories that remain very close to the optimal solution (Mikkelsen et al., 2024). The ADMM-based budget-trading method is roughly 8× slower than the centralized MR-CaTP of the prior method when ignoring message-passing latency, but it avoids the need to send full trajectories to all robots; it also produces net budget buyers and sellers, with support robots selling budget and most inspection robots buying it while moving toward POIs (Mikkelsen et al., 2024). In communication-aware deployment, DP-FMM incurs about +6% mission time and +14.7% distance relative to FMM, whereas DPA-FMM uses fewer robots and reduces total team distance by 23% but increases maximum path length by about 31%, with temporary disconnections around 3% of the time during multi-goal tours (Marchukov et al., 24 Mar 2025). For long-range UAV path planning, the constrained Theta* variant achieves relative path length 1.06 and success rate 98%, compared with LIAN-5 at relative path length 1.14 and success rate 87% (Sharma et al., 2017).

PISAC provides perhaps the clearest planning-level demonstration of planning-oriented resource distribution: at SNR $x_j$3 dB, PISAC attains 100% success rate, $x_j$4 pass time, and $x_j$5 trajectory length, while ISAC, SRM, and MMF achieve 60%, 50%, and 55% success rates respectively; the paper states that PISAC improves success rate by at least 40 percentage points relative to those baselines and reduces traversal time by more than 5% relative to the best baseline (Jin et al., 27 Oct 2025).

6. Limitations, misconceptions, and research directions

A persistent misconception is that communication-aware planning is synonymous with preserving graph connectivity. The surveyed work shows a much broader design space: some formulations optimize bandwidth availability, some optimize algebraic connectivity, some treat communication as control-center reachability, some distribute compression templates or beam powers, and some encode communication quality only through symbolic capacities or RSS thresholds (Zhang et al., 2022, Mikkelsen et al., 2024, Byeon et al., 2018, Psomiadis et al., 13 Mar 2025, Liu et al., 2017, Marchukov et al., 24 Mar 2025). This suggests that “communication-aware” is best understood as a coupling pattern between communication variables and task feasibility, rather than a single metric.

Another misconception is that mode distribution is always explicit. In several papers, modes are emergent rather than declared. Budget trading in ADMM-based trajectory planning yields task-focused versus support/relay behavior without hard-coded roles; EAP II and EAP III induce low-mobility or high-mobility behavior through the ratio $x_j$6; and Fiedler-constrained inspection planners cause some robots to become relay backbones because that is the only way to keep $x_j$7 above threshold (Mikkelsen et al., 2024, Jaleel et al., 2016, Mikkelsen et al., 2024). A plausible implication is that explicit role variables are sometimes unnecessary when the communication metric is sufficiently informative and the optimization architecture exposes per-agent marginal contributions.

The main limitations are equally consistent across domains. Many formulations assume static or quasi-static environments, centralized or globally synchronized information, holonomic or linearized dynamics, fixed template or power-level sets, and communication models that neglect latency, bandwidth, cyber-security, or failure detection. ORDPDC models connectivity but not latency or cyber-security; the STL/STREL and SpaTeL planners use bounded-time logic and MILP encodings but not detailed PHY models; the UAV planner assumes quasi-static connectivity maps; the map-compression framework assumes a static environment and a hand-designed template set; and the deployment framework allows temporary motion-time disconnections and relies on known RSS maps (Byeon et al., 2018, Liu et al., 2018, Liu et al., 2017, Sharma et al., 2017, Psomiadis et al., 13 Mar 2025, Marchukov et al., 24 Mar 2025). This suggests that future work will likely focus on multi-period dynamics, richer communication models, explicit failure handling, and learned or adaptive mode sets rather than on entirely new problem definitions.

At a methodological level, the dominant pattern is clear. Communication-aware mode distribution planning typically proceeds by: defining a communication-sensitive state representation; introducing mode or role variables, either explicit or implicit; coupling them to task objectives or safety constraints through SINR, RSS, Laplacian, CRB, bit-cost, or capacity models; and then using decomposition, sparsification, hierarchical MPC, branch-and-price, PSO, or graph search to recover tractable solutions. The literature therefore presents not a single algorithmic recipe but a mature family of cyber-physical planning formulations whose central invariant is that communication is modeled as a first-class planning variable rather than a background assumption (Jaleel et al., 2016, Wang et al., 2016, Mikkelsen et al., 2024, Jin et al., 27 Oct 2025).