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Representative Papers

On the Binary Rank of Matrices with Constant Real Rank

Sep 24, 2026

This study addresses the longstanding open problem in combinatorial optimization concerning upper bounds on the binary rank of matrices with fixed real rank, which has previously relied on computer-assisted verification without a general theoretical framework. By integrating techniques from linear algebra, combinatorics, and biclique partitioning of bipartite graphs in graph theory, this work proposes a purely mathematical proof strategy that eliminates the need for computational assistance, establishing a general framework for deriving upper bounds applicable to arbitrary fixed real ranks. The authors rigorously determine the maximum binary rank for matrices of real rank five, completely resolving this long-standing challenge. Furthermore, they establish non-trivial upper bounds on the binary rank of fixed-real-rank matrices and derive theoretical limits on the minimum number of edge biclique partitions in the corresponding bipartite graphs, providing a novel analytical paradigm for related research.

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Testing the Binary Rank with Polynomial Query Complexity

Sep 09, 2026

本文提出了一种具有多项式查询复杂度的自适应双边误差测试算法，用于检测0,1矩阵的二进制秩，并能进一步找到该矩阵的一个近似二进制分解。

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When Words Divide: Diachronic Ideological Polarization in Political Discourse on Social Media

Aug 02, 2026

This study addresses the lack of systematic understanding regarding the mechanisms driving the evolution of ideological polarization in long-term online political discourse. To overcome the limitations of cross-sectional or sentiment-focused analyses, this work proposes a temporally aligned, community-specific word embedding approach that integrates semantic distance metrics with large-scale Reddit discussion data. For the first time, this framework enables longitudinal modeling of semantic divergence between opposing political groups on key concepts. Empirical results demonstrate a significant intensification of ideological polarization at both conceptual and topical levels over the study period, confirming the method’s capacity to effectively capture dynamic polarization processes in large-scale textual corpora.

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Fair Allocation under Conflict Constraints via Strong Colorability

Jul 01, 2026

This work addresses the problem of fairly allocating vertices of a graph among multiple agents with identical preferences under conflict constraints, where adjacent vertices cannot be assigned to the same agent. The authors introduce, for the first time, a hierarchical framework based on the strong chromatic number to unify the modeling of fair allocation under three fairness criteria: SD-EF1, EF1, and EF[1,1]. Leveraging techniques from strong graph coloring, they design a deterministic polynomial-time algorithm whose performance depends on the graph’s maximum degree Δ. They prove that for any graph with maximum degree Δ, a fair allocation satisfying all three criteria exists whenever the number of agents is at least 3Δ−1. Moreover, when the number of agents is at least (3+ε)Δ for any constant ε>0, such an allocation can be efficiently constructed.

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Setwise Distinguishable Permutations

Jun 19, 2026

This work investigates the construction of maximum-sized families of set-distinguishable permutations—collections in which each permutation admits a subset whose image under that permutation is distinct from its image under any other permutation in the family. Through an explicit combinatorial construction, the authors achieve a family size of $2^{(2 - o(1))n}$, asymptotically approaching the theoretical upper bound. This construction is applied for the first time to analyze conditional kernelization lower bounds for graph coloring parameterized by the vertex-deletion distance to split graphs, yielding nearly tight complexity lower bounds that substantially improve upon the prior results of Jansen and Kratsch (2013).

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Latest Papers

On the Binary Rank of Matrices with Constant Real Rank

Sep 24, 2026

This study addresses the longstanding open problem in combinatorial optimization concerning upper bounds on the binary rank of matrices with fixed real rank, which has previously relied on computer-assisted verification without a general theoretical framework. By integrating techniques from linear algebra, combinatorics, and biclique partitioning of bipartite graphs in graph theory, this work proposes a purely mathematical proof strategy that eliminates the need for computational assistance, establishing a general framework for deriving upper bounds applicable to arbitrary fixed real ranks. The authors rigorously determine the maximum binary rank for matrices of real rank five, completely resolving this long-standing challenge. Furthermore, they establish non-trivial upper bounds on the binary rank of fixed-real-rank matrices and derive theoretical limits on the minimum number of edge biclique partitions in the corresponding bipartite graphs, providing a novel analytical paradigm for related research.

0 citationsRead paper

Testing the Binary Rank with Polynomial Query Complexity

Sep 09, 2026

本文提出了一种具有多项式查询复杂度的自适应双边误差测试算法，用于检测0,1矩阵的二进制秩，并能进一步找到该矩阵的一个近似二进制分解。

0 citationsRead paper

When Words Divide: Diachronic Ideological Polarization in Political Discourse on Social Media

Aug 02, 2026

This study addresses the lack of systematic understanding regarding the mechanisms driving the evolution of ideological polarization in long-term online political discourse. To overcome the limitations of cross-sectional or sentiment-focused analyses, this work proposes a temporally aligned, community-specific word embedding approach that integrates semantic distance metrics with large-scale Reddit discussion data. For the first time, this framework enables longitudinal modeling of semantic divergence between opposing political groups on key concepts. Empirical results demonstrate a significant intensification of ideological polarization at both conceptual and topical levels over the study period, confirming the method’s capacity to effectively capture dynamic polarization processes in large-scale textual corpora.

0 citationsRead paper

Fair Allocation under Conflict Constraints via Strong Colorability

Jul 01, 2026

This work addresses the problem of fairly allocating vertices of a graph among multiple agents with identical preferences under conflict constraints, where adjacent vertices cannot be assigned to the same agent. The authors introduce, for the first time, a hierarchical framework based on the strong chromatic number to unify the modeling of fair allocation under three fairness criteria: SD-EF1, EF1, and EF[1,1]. Leveraging techniques from strong graph coloring, they design a deterministic polynomial-time algorithm whose performance depends on the graph’s maximum degree Δ. They prove that for any graph with maximum degree Δ, a fair allocation satisfying all three criteria exists whenever the number of agents is at least 3Δ−1. Moreover, when the number of agents is at least (3+ε)Δ for any constant ε>0, such an allocation can be efficiently constructed.

0 citationsRead paper

Setwise Distinguishable Permutations

Jun 19, 2026

This work investigates the construction of maximum-sized families of set-distinguishable permutations—collections in which each permutation admits a subset whose image under that permutation is distinct from its image under any other permutation in the family. Through an explicit combinatorial construction, the authors achieve a family size of $2^{(2 - o(1))n}$, asymptotically approaching the theoretical upper bound. This construction is applied for the first time to analyze conditional kernelization lower bounds for graph coloring parameterized by the vertex-deletion distance to split graphs, yielding nearly tight complexity lower bounds that substantially improve upon the prior results of Jansen and Kratsch (2013).

0 citationsRead paper