arXiv subjects
Publications and source records attributed to Jianping Pan.
In a previous work, we defined (type A) c-Birkhoff polytopes and showed that they were unimodularly equivalent to order polytopes of heap posets. In this note we answer the question: What about type B?
We revisit combinatorial Thompson sampling (CTS) for semi-bandits with sleeping arms, where arm availability varies over time and actions must satisfy combinatorial constraints, as in wireless mesh routing with fluctuating link availability. Despite its practical relevance, CTS has been hindered by several long-standing problems: (i) the absence of worst-case regret guarantees in the semi-bandit setting even without sleeping arms, (ii) the lack of theory under adversarially varying availability, and (iii) the consistently weak empirical performance of CTS with Gaussian priors (CTS-G). This paper resolves these long-standing issues by providing the first worst-case regret analysis of CTS-G, proving an upper bound of $\tilde{O}(m\sqrt{NT})$ and a matching lower bound of $\tilde{\Omega}(m\sqrt{NT})$. To bridge the gap between theory and practice, we further propose CL-SG, a simple CTS-G variant that samples a single shared Gaussian seed each round to coordinate exploration across arms. We show that CL-SG achieves an improved regret bound of $\tilde{O}(\sqrt{mNT})$, together with a matching lower bound $\Omega(\sqrt{mNT})$. Experiments on real-world datasets demonstrate that CL-SG consistently outperforms strong baselines including CTS-G and CTS-B, and we open-source our implementation for reproducibility.
In the last few years, considerable research efforts have focused on measuring and improving Starlink network performance, especially for user terminals (UTs) in stationary scenarios. However, the performance of Starlink networks in mobility settings, particularly with frequent changes in the UT's orientation, and the impact of environmental factors, such as transient obstructions, has not been thoroughly studied, leaving gaps in understanding the causes of performance degradation. Recently, researchers have started identifying the communicating satellites to evaluate satellite selection strategies and the impact on network performance. However, existing Starlink satellite identification methods only work in stationary, obstruction-free scenarios, as they do not account for UT mobility, obstructions or detect dynamic beam switching events. In this paper, we reveal that the UT can perform multiple dynamic beam switching attempts to connect to different satellites when the UT-satellite link is degraded. This degradation can occur either due to the loss of line-of-sight (LoS) from changes in the FOV or obstructions, or due to poor signal quality, extending UT-satellite handovers beyond the well-known 15-second regular handover interval. We propose a mobility-aware Starlink satellite identification method that detects dynamic beam switching events, and plausibly explain network performance using UT's diagnostic data and connected satellite information. Our findings demystifies the mobile Starlink network performance degradations, which is crucial to enhance the end-to-end performance of transport layer protocols and in diverse application scenarios.
The rapid expansion of LEO satellite constellations has enabled an integrated terrestrial network and non-terrestrial network (TN-NTN), connecting diverse users such as aircraft, ships, and remote communities. These networks increasingly need a scalable and efficient multicast protocol for critical applications like emergency alerts, large-scale software updates, and real-time broadcasting. However, traditional multicast protocols, such as IP-based multicast and software-defined multicast approaches, introduce significant control overhead and struggle to adapt to the dynamic and mobile nature of satellite topologies. This paper presents BIER-Star, a stateless multicast protocol designed for the integrated TN-NTN. BIER-Star uses a two-layer geospatial gridding scheme (i.e., H3) to encode destinations as Earth- and space-cell identifiers rather than per-terminal addresses. This cell-based abstraction shortens the header bitstring, simplifies forwarding, and eliminates per-flow state and complex signaling. Our simulations indicate that BIER-Star reduces header size versus BIER and avoids geographic path-finding failures seen in greedy methods.
The analytical characterization of coverage probability in finite three-dimensional wireless networks has long remained an open problem, hindered by the loss of spatial independence in finite-node settings and the coupling between link distances and interference in bounded geometries. This paper closes this gap by presenting the first exact analytical framework for coverage probability in finite 3D networks modeled by a binomial point process within a cylindrical region. To bypass the intractability that has long hindered such analyses, we leverage the independence structure, convolution geometry, and derivative properties of Laplace transforms, yielding a formulation that is both mathematically exact and computationally efficient. Extensive Monte Carlo simulations verify the analysis and demonstrate significant accuracy gains over conventional Poisson-based models. The results generalize to any confined 3D wireless system, including aerial, underwater, and robotic networks.
We study the monoid algebra ${}_{n}\mathcal{T}_{m}$ of semistandard Young tableaux, which coincides with the Gelfand--Tsetlin semigroup ring $\mathcal{GT}_{n}$ when $m = n$. Among others, we show that this algebra is commutative, Noetherian, reduced, Koszul, and Cohen--Macaulay. We provide a complete classification of its maximal ideals and compute the topology of its maximal spectrum. Furthermore, we classify its irreducible modules and provide a faithful semisimple representation. We also establish that its associated variety coincides with a toric degeneration of certain partial flag varieties constructed by Gonciulea--Lakshmibai. As an application, we show that this algebra yields injective embeddings of $\mathfrak{sl}_n$-crystals, extending a result of Bossinger--Torres.
Low Earth Orbit (LEO) satellite ISPs promise universal Internet connectivity, yet their interaction with content delivery remains poorly understood. We present the first comprehensive measurement study decomposing Starlink's web content delivery performance decomposed across Point of Presence (PoP), DNS, and CDN layers. Through two years of measurements combining 225K Cloudflare AIM tests, M-Lab data, and active probing from 99 RIPE Atlas and controlled Starlink probes, we collect 6.1M traceroutes and 10.8M DNS queries to quantify how satellite architecture disrupts terrestrial CDN assumptions. We identify three distinct performance regimes based on infrastructure density. Regions with local content-rich PoPs achieve near-terrestrial latencies with the satellite segment dominating 80-90% of RTT. Infrastructure-sparse regions suffer cascading penalties: remote PoPs force distant resolver selection, which triggers CDN mis-localization, pushing latencies beyond 200 ms. Dense-infrastructure regions show minimal sensitivity to PoP changes. Leveraging Starlink's infrastructure expansion in early 2025 as a natural experiment, we demonstrate that relocating PoPs closer to user location reduces median page-fetch times by 60%. Our findings reveal that infrastructure proximity, not satellite coverage, influences web performance, requiring fundamental changes to CDN mapping and DNS resolution for satellite ISPs.
Motivated by the question of which structural properties of a graph can be recovered from the chromatic symmetric function (CSF), we study the CSF of connected unicyclic graphs. While it is known that there can be non-isomorphic unicyclic graphs with the same CSF, we find experimentally that such examples are rare for graphs with up to 17 vertices. In fact, in many cases we can recover data such as the number of leaves, number of internal edges, cycle size, and number of attached non-trivial trees, by extending known results for trees to unicyclic graphs. These results are obtained by analyzing the CSF of a connected unicyclic graph in the $\textit{star-basis}$ using the deletion-near-contraction (DNC) relation developed by Aliste-Prieto, Orellana and Zamora, and computing the "leading" partition, its coefficient, as well as coefficients indexed by hook partitions. We also give explicit formulas for star-expansions of several classes of graphs, developing methods for extracting coefficients using structural properties of the graph.
In a 2018 paper, Davis and Sagan studied several pattern-avoiding polytopes. They found that a particular pattern-avoiding Birkhoff polytope had the same normalized volume as the order polytope of a certain poset, leading them to ask if the two polytopes were unimodularly equivalent. Motivated by Davis and Sagan's question, in this paper we define a pattern-avoiding Birkhoff polytope called a $c$-Birkhoff polytope for each Coxeter element $c$ of the symmetric group. We then show that the $c$-Birkhoff polytope is unimodularly equivalent to the order polytope of the heap poset of the $c$-sorting word of the longest permutation. When $c=s_1s_2\dots s_{n}$, this result recovers an affirmative answer to Davis and Sagan's question. Another consequence of this result is that the normalized volume of the $c$-Birkhoff polytope is the number of the longest chains in the (type A) $c$-Cambrian lattice.
We study Type C $K$-Stanley symmetric functions, which are $K$-theoretic extensions of the Type C Stanley symmetric functions. They are indexed by signed permutations and can be used to enumerate reduced words via their expansion into Schur $Q$-functions, which are indexed by strict partitions. A combinatorial description of the Schur $Q$- coefficients is given by Kra\'skiewicz insertion. Similarly, their $K$-Stanley analogues are conjectured to expand positively into $GQ$'s, which are $K$-theory representatives for the Lagrangian Grassmannian introduced by Ikeda and Naruse also indexed by strict partitions. We introduce a $K$-theoretic analogue of Kra\'skiewicz insertion, which can be used to enumerate 0-Hecke expressions for signed permutations and gives a conjectural combinatorial rule for computing this $GQ$ expansion. We show the Type C $K$-Stanleys for certain fully commutative signed permutations are skew $GQ$'s. Combined with a Pfaffian formula of Anderson's, this allows us to prove Lewis and Marberg's conjecture that $GQ$'s of (skew) rectangle shape are $GQ$'s of trapezoid shape. Combined with our previous conjecture, this also gives an explicit combinatorial description of the skew $GQ$ expansion into $GQ$'s. As a consequence, we obtain a conjecture for the product of two $GQ$ functions where one has trapezoid shape.
Refined canonical stable Grothendieck polynomials were introduced by Hwang, Jang, Kim, Song, and Song. There exist two combinatorial models for these polynomials: one using hook-valued tableaux and the other using pairs of a semistandard Young tableau and (what we call) an exquisite tableau. An uncrowding algorithm on hook-valued tableaux was introduced by Pan, Pappe, Poh, and Schilling. In this paper, we discover a novel connection between the two models via the uncrowding and Goulden--Greene's jeu de taquin algorithms, using a classical result of Benkart, Sottile, and Stroomer on tableau switching. This connection reveals a symmetry of the uncrowding algorithm defined on hook-valued tableaux. As a corollary, we obtain another combinatorial model for the refined canonical stable Grothendieck polynomials in terms of biflagged tableaux, which naturally appear in the characterization of the image of the uncrowding map.
System-level performance evaluation over satellite networks often requires a simulated or emulated environment for reproducibility and low cost. However, the existing tools may not meet the needs for scenarios such as the low-earth orbit (LEO) satellite networks. To address the problem, this paper proposes and implements a trace-driven emulation method based on Linux's eBPF technology. Building a Starlink traces collection system, we demonstrate that the method can effectively and efficiently emulate the connection conditions, and therefore provides a means for evaluating applications on local hosts.
Secure and privacy-preserving data aggregation in the Internet of Vehicles (IoV) continues to be a focal point of interest in both the industry and academia. Aiming at tackling the challenges and solving the remaining limitations of existing works, this paper introduces a novel Schnorr approval-based IoV data aggregation framework based on a two-layered architecture. In this framework, a server can aggregate the IoV data from clusters without inferring the raw data, real identity and trajectories of vehicles. Notably, we avoid incorporating the widely-accepted techniques such as homomorphic encryption and digital pseudonym to avoid introducing high computation cost to vehicles. We propose a novel concept, data approval, based on the Schnorr signature scheme. With the approval, the fake data injection attack carried out by a cluster head can be defended against. The separation of liability is achieved as well. The evaluation shows that the framework is secure and lightweight for vehicles in terms of the computation and communication costs.
A leading industry standard for secure and trusted communication in vehicular ad-hoc networks (VANETs) is the Security Credential Management System (SCMS). It uses anonymous certificates, functioning as pseudonyms, to preserve the privacy of vehicles. With the rapid development of advanced applications in VANETs, such as crowdsensing and federated learning, vehicles need to communicate with each other or infrastructures more frequently, leading to a higher demand for pseudonyms. However, the current approach of certificate provisioning in SCMS is not able to fully support pseudonyms, due to storage limitation, cost of connectivity establishment, and communication overhead of certificate downloading. To tackle this challenge, we propose a non-interactive approach for SCMS, allowing vehicles themselves to generate short-term key pairs and anonymous implicit certificates. Our evaluation and comparison with previous work show that our solution not only effectively reduces the communication cost, but also grants vehicles greater flexibility in certificate generation and use. On the technical side, to the best of our knowledge, this is the first work which (1) applies sanitizable signature for non-interactive anonymous certificate generation, and (2) is specifically designed for SCMS, which opens up possibilities for extensions and applications in industry.
Starlink and alike have attracted a lot of attention recently, however, the inner working of these low-earth-orbit (LEO) satellite networks is still largely unknown. This paper presents an ongoing measurement campaign focusing on Starlink, including its satellite access networks, gateway and point-of-presence structures, and backbone and Internet connections, revealing insights applicable to other LEO satellite providers. It also highlights the challenges and research opportunities of the integrated space-air-ground-aqua network envisioned by 6G mobile communication systems, and calls for a concerted community effort from practical and experimentation aspects.
Air pollution has become a global concern for many years. Vehicular crowdsensing systems make it possible to monitor air quality at a fine granularity. To better utilize the sensory data with varying credibility, truth discovery frameworks are introduced. However, in urban cities, there is a significant difference in traffic volumes of streets or blocks, which leads to a data sparsity problem for truth discovery. Protecting the privacy of participant vehicles is also a crucial task. We first present a data masking-based privacy-preserving truth discovery framework, which incorporates spatial and temporal correlations to solve the sparsity problem. To further improve the truth discovery performance of the presented framework, an enhanced version is proposed with anonymous communication and data perturbation. Both frameworks are more lightweight than the existing cryptography-based methods. We also evaluate the work with simulations and fully discuss the performance and possible extensions.
The Castelnuovo-Mumford polynomial $\widehat{\mathfrak{G}}_w$ with $w \in S_n$ is the highest homogeneous component of the Grothendieck polynomial $\mathfrak{G}_w$. Pechenik, Speyer and Weigandt define a statistic $\mathsf{rajcode}(\cdot)$ on $S_n$ that gives the leading monomial of $\widehat{\mathfrak{G}}_w$. We introduce a statistic $\mathsf{rajcode}(\cdot)$ on any diagram $D$ through a combinatorial construction ``snow diagram'' that augments and decorates $D$. When $D$ is the Rothe diagram of a permutation $w$, $\mathsf{rajcode}(D)$ agrees with the aforementioned $\mathsf{rajcode}(w)$. When $D$ is the key diagram of a weak composition $\alpha$, $\mathsf{rajcode}(D)$ yields the leading monomial of $\widehat{\mathfrak{L}}_\alpha$, the highest homogeneous component of the Lascoux polynomials $\mathfrak{L}_\alpha$. We use $\widehat{\mathfrak{L}}_\alpha$ to construct a basis of $\widehat{V}_n$, the span of $\widehat{\mathfrak{G}}_w$ with $w \in S_n$. Then we show $\widehat{V}_n$ gives a natural algebraic interpretation of a classical $q$-analogue of Bell numbers.
For each fully commutative permutation, we construct a "boolean core," which is the maximal boolean permutation in its principal order ideal under the right weak order. We partition the set of fully commutative permutations into the recently defined crowded and uncrowded elements, distinguished by whether or not their RSK insertion tableaux satisfy a sparsity condition. We show that a fully commutative element is uncrowded exactly when it shares the RSK insertion tableau with its boolean core. We present the dynamics of the right weak order on fully commutative permutations, with particular interest in when they change from uncrowded to crowded. In particular, we use consecutive permutation patterns and descents to characterize the minimal crowded elements under the right weak order.