离散数学

Given a graph $G$ and two independent sets of $G$, the independent set reconfiguration problem asks whether one independent set can be transformed into the other by moving a single vertex at a time, such that at each intermediate step we…

Dominant areas of computer science and computation systems are intensively linked to the hypercube-related studies and interpretations. This article presents some transformations and analytics for some example algorithms and Boolean domain…

In this work, we describe a method that determines an exact map from a finite set of subgraph densities to the parameters of a stochastic block model (SBM) matching these densities. Given a number $K$ of blocks, the subgraph densities of a…

We consider the task of allocating indivisible items to agents, when the agents' preferences over the items are identical. The preferences are captured by means of a directed acyclic graph, with vertices representing items and an edge…

The forcing number of a graph with a perfect matching $M$ is the minimum number of edges in $M$ whose endpoints need to be deleted, such that the remaining graph only has a single perfect matching. This number is of great interest in…

Transit functions serve not only as abstractions of betweenness and convexity but are also closely connected with clustering systems. Here, we investigate the canonical transit functions of binary clustering systems inspired by pyramids,…

Can a list of binary strings be ordered so that consecutive strings differ in a single bit? Can a list of permutations be ordered so that consecutive permutations differ by a swap? Can a list of non-crossing set partitions be ordered so…

We study straight-line drawings of graphs where the vertices are placed in convex position in the plane, i.e., \emph{convex drawings}. We consider two families of graph classes with convex drawings: \emph{outer $k$-planar} graphs, where…

In this paper we address the problem of allocating the efforts of a collection of repairmen to a number of deteriorating machines in order to reduce operation costs and to mitigate the cost (and likelihood) of unexpected failures.…

Though a core element of the digital age, numerical difference algorithms struggle with noise susceptibility. This stems from a key disconnect between the infinitesimal quantities in continuous differentiation and the finite intervals in…

In this work we introduce and study a pursuit-evasion game in which the search is performed by heterogeneous entities. We incorporate heterogeneity into the classical edge search problem by considering edge-labeled graphs: once a search…

We study shared processor scheduling of $\textit{multiprocessor}$ weighted jobs where each job can be executed on its private processor and simultaneously on possibly $\textit{many}$ processors shared by all jobs in order to reduce their…

The classic question of whether one should walk or run in the rain to remain the least wet has inspired a myriad of solutions ranging from physically performing test runs in raining conditions to mathematically modeling human movement…

This work is thought as an operative guide to discrete exterior calculus (DEC), but at the same time with a rigorous exposition. We present a version of (DEC) on cubic cell, defining it for discrete manifolds. An example of how it works, it…

We present a general framework to generate trees every vertex of which has a non-negative weight and a color. The colors are used to impose certain restrictions on the weight and colors of other vertices. We first extend the enumeration…

Generating random and pseudorandom numbers with a deterministic system is a long-standing challenge in theoretical research and engineering applications. Several pseudorandom number generators based on the inversive congruential method have…

Many countries around the world, including Korea, use the school choice lottery system. However, this method has a problem in that many students are assigned to less-preferred schools based on the lottery results. In addition, the task of…

We prove that a polynomial fraction of the set of $k$-component forests in the $m \times n$ grid graph have equal numbers of vertices in each component, for any constant $k$. This resolves a conjecture of Charikar, Liu, Liu, and Vuong, and…

A proper Helly circular-arc graph is an intersection graph of a set of arcs on a circle such that none of the arcs properly contains any other arc and every set of pairwise intersecting arcs has a common intersection. The Proper Helly…

In this work, we show that the class of word-representable graphs is closed under split recomposition and determine the representation number of the graph obtained by recomposing two word-representable graphs. Accordingly, we show that the…