A vertex coloring c : V(G) → ℕ of a non-trivial graph G is called a sigma coloring if σ(u) ≠ σ(v) for any pair of adjacent vertices u and v. Here, σ(x) denotes the sum of the colors assigned to vertices adjacent to x. The sigma chromatic number of G, denoted by σ(G), is defined as the fewest number of colors needed to construct a sigma coloring of G. In this paper, we consider the sigma chromatic number of graphs obtained by deleting one or more of its edges. In particular, we study the difference σ(G) - σ(G-e) in general as well as in restricted scenarios; here, G - e is the graph obtained by deleting an edge e from G. Furthermore, we study the sigma chromatic number of graphs obtained via multiple edge deletions in complete graphs by considering the complements of paths and cycles.

Let G be a nontrivial connected graph of order n. Let k be an integer with 2 ≤ k ≤ n. A strong k-rainbow coloring of G is an edge-coloring of G having property that for every set S of k vertices of G, there exists a tree with minimum size containing S whose all edges have distinct colors. The minimum number of colors required such that G admits a strong k-rainbow coloring is called the strong k-rainbow index srx_k(G) of G. In this paper, we study the strong 3-rainbow index of comb product between a tree and a connected graph, denoted by T_n ⊳_o H. Notice that the size of T_n ⊳_o H is the trivial upper bound for srx₃(T_n ⊳_o H), which means we can assign distinct colors to all edges of T_n ⊳_o H. However, there are some connected graphs H such that some edges of T_n ⊳_o H may be colored the same. Therefore, in this paper, we characterize connected graphs H with srx₃(T_n ⊳_o H) = |E(T_n ⊳_o H)|. We also provide a sharp upper bound for srx₃(T_n ⊳_o H) where srx₃(T_n ⊳_o H) ≠ |E(T_n ⊳_o H)|. In addition, we determine the srx₃(T_n ⊳_o H) for some connected graphs H.

We utilize the hardness of the Unambiguous-SAT problem under randomized polynomial time reductions (Valiant & Vazirani; Theoret. Comput. Sci., Vol.47, 1986) to probe the required properties of counterexamples to open non-existence conjectures for uniquely Hamiltonian graphs under various topological constraints. Concerning ourselves with a generalization of Sheehan's 1975 conjecture that no uniquely Hamiltonian graphs exist in the class of (r ∈ 2 ℕ_>1)-regular graphs (for 4 ≤ r ≤ 22), Bondy & Jackson's 1998 conjecture that no uniquely Hamiltonian graphs exist in the class of planar graphs having at most one vertex of degree ≤ 2, and Fleischner's 2014 conjecture that no uniquely Hamiltonian graphs exist in the class of 4-vertex-connected graphs, we prove that each conjecture is false if and only if there exists a parsimonious reduction from #SAT to counting Hamiltonian cycles on each graph class in question. As the existence of such a reduction allows for the encoding of arbitrary Unambiguous-SAT problem instances, by the Valiant-Vazirani theorem we have that hypothetical sets of counterexamples for each non-existence conjecture cannot belong to any graph class with a polynomial time testable property implying tractability for the Hamiltonian cycle decision problem (unless NP = RP).

In this paper, we study the problem of gossiping with neighboring interference constraint in radio chain networks. Gossiping (also called total exchange information) is a protocol where each node in the network has a message and is expected to distribute its own message to every other node in the network. The gossiping problem consists in finding the minimum running time (makespan) of a gossiping protocol and efficient algorithms that attain this makespan. We focus on the case where the transmission network is a chain (directed path or line) network. We consider synchronous protocols where it takes one unit of time (step) to transmit a unit-length message. During one step, a node receives at most one message only through one of its two neighbors. We assume that during one step, a node cannot be both a sender and a receiver (half duplex model). Moreover we have neighboring interference constraints under which a node cannot receive a message if one of its neighbors is sending. A round consists of a set of non-interfering (or compatible) calls and uses one step. We completely solve the gossiping problem for P_n, the chain network on n nodes, and give an algorithm that completes the gossiping in 3n - 5 rounds (for n > 3), which is exactly the makespan.

An associative magic square is a magic square such that the sum of any 2 cells at symmetric positions with respect to the center is constant. The total number of associative magic squares of order 7 is enormous and thus, it is not realistic to obtain the number by simple backtracking. As a recent result, Ripatti reported the number of semi-magic squares of order 6 (the magic squares of 6 × 6 without diagonal sum conditions) in 2018. In this research, with reference to Ripatti's method of enumerating semi-magic squares, we have calculated the total number of associative magic squares of order 7. There are exactly 1,125,154,039,419,854,784 associative magic squares of order 7 excluding symmetric patterns.

The Creek puzzle is a pencil-and-paper puzzle developed by Japanese puzzle publisher Nikoli, usually played on a square grid. We study the computational complexity of the Creek puzzle, and first it is shown that deciding whether a given instance of this puzzle on a square grid has a solution is NP-complete by a reduction from the Circuit-SAT problem. In addition, we prove the NP-completeness for the Creek puzzle on triangular grids in the same way.

We consider the computational complexity of winning this turn (mate-in-1 or “finding lethal”) in Hearthstone as well as several other single turn puzzle types introduced in the Boomsday Lab expansion. We consider three natural generalizations of Hearthstone (in which hand size, board size, and deck size scale) and prove the various puzzle types in each generalization NP-hard.

We prove PSPACE-completeness of all but one problem in a large space of pulling-block problems where the goal is for the agent to reach a target destination. The problems are parameterized by whether pulling is optional, the number of blocks which can be pulled simultaneously, whether there are fixed blocks or thin walls, and whether there is gravity. We show NP-hardness for the remaining problem, Pull?-1FG (optional pulling, strength 1, fixed blocks, with gravity).

We prove that the classic falling-block video game Tetris (both survival and board clearing) remains NP-complete even when restricted to 8 columns, or to 4 rows, settling open problems posed over 15 years ago. Our reduction is from 3-Partition, similar to the previous reduction for unrestricted board sizes, but with a better packing of buckets. On the positive side, we prove that 2-column Tetris (and 1-row Tetris) is polynomial. We also prove that the generalization of Tetris to larger k-omino pieces is NP-complete even when the board starts empty, and even when restricted to 3 columns or 2 rows or constant-size pieces. Finally, we present an animated Tetris font.

“Slitherlink” is one of popular pencil puzzles. The purpose of the puzzle is to make a link according to the digits written in cells. While determining the existence of a solution to a given puzzle is proved to be an NP-complete class of problems, which means it is difficult to find an effective algorithm to solve the puzzle, solving the puzzle has been studied and there are several previous researches for the puzzle. In this paper, we show two new methods to solve the puzzle. One is with hardware acceleration on an FPGA and the other is based on an SMT solver. We focus on determining inside or outside for each cell instead of making a link and propose a new formulation. With hardware acceleration, it takes 0.1578 seconds on average for solving 10 × 10 puzzles, and with an SMT solver, our solution is faster than previous researches in most cases.

This article presents an impartial game, “Corner Two Rooks.” This game is a variant of “Corner the Queen” that is mathematically equivalent to Wythoff's game. In “Corner the Queen, ” a single chess queen is placed on a large grid of squares. Each player can move the queen any number of steps toward the upper-left corner of the grid, vertically, horizontally, or diagonally. The player who moves the queen into the upper-left corner is the winner. In this work, the authors use two rooks of chess instead of the queen, and a rook can jump over another rook but not onto another. There is a restriction on the distance that a rook can travel in each turn. This game can be considered as a misère game of the traditional Nim game with four piles and a restriction of the number of stones to be removed in each turn. The authors present the set of P-positions of the game using a theorem for misère games. When there is no restriction on the distance that a rook can travel in each turn, we obtain a similar result in which the set of P-positions is simpler.

We study the game-theoretical structure of a scenario where a decision maker has to determine locations of stations in a transportation system. We introduce a new model on facility games, called the “shuttle facility game.” A facility F is defined to be an interval with two stations over a transportation line. Then, the decision maker wishes to design a mechanism that given as input a set of intervals reported by each player, where I_i represents the commuting route of player i, determines a location for F. The profit of a facility location is defined based on the “convenience” to each player, such as the distance to the facility. A player i may try to manipulate the output of the mechanism by strategically misreporting I_i to get a higher profit. We formulate two shuttle facility games: the fixed-length and the flexible-length shuttle facility game; and prove that each admits a group strategy-proof mechanism. We prove that the social profit is also maximized by a location of F determined by our group strategy-proof mechanism, that is, a decision maker can find a location of F so that the social profit is maximized and group strategy-proofness is attained at the same time.

We analyze the computational complexity of several new variants of edge-matching puzzles. First we analyze inequality (instead of equality) constraints between adjacent tiles, proving the problem NP-complete for strict inequalities but polynomial-time solvable for nonstrict inequalities. Second we analyze three types of triangular edge matching, of which one is polynomial-time solvable and the other two are NP-complete; all three are #P-complete. Third we analyze the case where no target shape is specified and we merely want to place the (square) tiles so that edges match exactly; this problem is NP-complete. Fourth we consider four 2-player games based on 1 × n edge matching, all four of which are PSPACE-complete. Most of our NP-hardness reductions are parsimonious, newly proving #P and ASP-completeness for, e.g., 1 × n edge matching. Along the way, we prove #P- and ASP-completeness of planar 3-regular directed Hamiltonicity; we provide linear-time algorithms to find antidirected and forbidden-transition Eulerian paths; and we characterize the complexity of new partizan variants of the Geography game on graphs.

Model extraction attacks are an attack in which an adversary utilizes a query access to the target model to obtain a new model whose performance is equivalent to the target model efficiently, i.e., fewer datasets and computational resources than those of the target model. Existing works have dealt with only simple deep neural networks (DNNs), e.g., only three layers, as targets of model extraction attacks, and hence are not aware of the effectiveness of recurrent neural networks (RNNs) in dealing with time-series data. In this work, we shed light on the threats of model extraction attacks on RNNs. We discuss whether a model with a higher accuracy can be extracted with a simple RNN from a long short-term memory (LSTM), which is a more complicated and powerful type of RNN. Specifically, we tackle the following problems. First, in case of a classification task, such as image recognition, extraction of an RNN model without final outputs from an LSTM model is presented by utilizing outputs halfway through the sequence. Next, in case of a regression task such as weather forecasting, a new attack by newly configuring a loss function is presented. We conduct experiments on our model extraction attacks on an RNN and an LSTM trained with publicly available academic datasets. We then show that a model with a higher accuracy can be extracted efficiently, especially through configuring a loss function and a more complex architecture different from the target model.

In order to keep up with the increasing number of cyberattacks, the defense tactics require timely and accurate understanding of the threats and corresponding risks. We propose a scheme for modeling threat information to extract event information from security reports on a paragraph basis and then estimate their kill chain phases. The experimental results show that the model got an average F1-score of 0.67, the average accuracy of 65% of the cyber kill chain phases and 86% of core features can be extracted by using this method.

Online service providers exert tremendous effort to protect users' accounts against sensitive data breaches. Although threats from complete outsiders, such as account hijacking for monetization, still occur, recent studies have shed light on threats to privacy from insiders. In this study, we focus on these latter threats. Specifically, we present the first comprehensive study of an attack from insiders that identifies the existence of a target's account by using the target's email address and the insecure login-related messages that are displayed. Such a threat may violate intimates' or acquaintances' privacy because the kinds of service accounts a user has implies his/her personal preferences or situation. We conducted surveys regarding user expectations and behaviors on online services and an extensive measurement study of login-related messages on online services that are considered sensitive. We found that over 80% of participants answered that they have sensitive services and that almost all services were vulnerable to our attack. Moreover, about half the participants who have sensitive services were insecurely registered on them, thus could be potential victims. Finally, we recommend ways for online service providers to improve login-related messages and for users to take appropriate defensive actions. We also report our responsible disclosure process.

Consider a simple undirected graph G = (V, E) with vertex set V and edge set E. The distance δ_G(x, y) is defined as the length of the shortest path between vertices x and y in G. The vertex u ∈ V is a hinge vertex if there exist two vertices x, y ∈ V - {u} such that δ_{G - u}(x, y) > δ_G(x, y). Let U be a set consisting of all hinge vertices of G, and let AVS(u) denote the set of pairs of vertices (x, y)s to which a path between x and y becomes longer after removal of a hinge vertex u from G. The influential hinge vertex problem aims to determine the hinge vertex u that maximizes |AVS(u)| in G. In this study, we propose an algorithm that runs in O(n²) time to solve the influential hinge vertex problem on an interval graph.

In targeted attacks, various malicious tools are leveraged by attackers. According to the Cybersecurity and Infrastructure Security Agency (CISA), tools such as China Chopper, Mimikatz, PowerShell Empire, and HUC Packet Transmitter are used in targeted attacks. Standard malware detection methods include those based on file names or hashes. However, attackers tend to avoid detection by changing the file name of malicious tools or by rebuilding them. Therefore, detecting malicious tools used in targeted attacks is difficult. We found that the order of Windows built-in DLLs loaded by each malicious tool has unique characteristics. In this study, we propose a detection method of malicious tools by analyzing DLL information using deep learning, considering the DLL and its order of loading by each process. We confirmed that even if the file names are changed or tools are rebuilt, our proposed method could detect the mentioned four tools with high detection rates: with a recall rate of 97.45%, a precision rate of 97.29%, and F value of 97.37% on average. Furthermore, the proposed method can detect malicious tools with more than a 90% detection rate, even if about 10% of loaded DLLs are changed in the future.

Achieving safe evacuation is the main goal of selecting an evacuation route. General path-finding methods determine a single shortest route to one end point; however, this is insufficient for selecting evacuation routes. Central Tokyo has a dense population with many tourists, and there are many areas with high disaster risk, such as densely populated wooden houses. As a result, it is important to prepare multiple evacuation sites and routes in case the optimal ones become unavailable. At present, the safety of evacuation routes is determined empirically; however, it should also be evaluated by quantitatively comparing multiple evacuation route candidates. In this paper, we propose a method for simultaneously deriving multiple evacuation route candidates using the Physarum solver. This method also quantitatively considers disaster risk. To evaluate the safety of the evacuation routes derived by this method, we define an index called the evacuation success rate. By developing a method for obtaining multiple evacuation routes considering disaster risk and by providing an index for quantitatively evaluating the safety of the obtained evacuation routes, safe and rapid evacuation can be achieved during disasters.

Field-programmable gate arrays (FPGAs) have garnered significant interest in research on high-performance computing because their computation and communication capabilities have drastically improved in recent years due to advances in semiconductor integration technologies that rely on Moore's Law. In addition to improving FPGA performance, toolchains for the development of FPGAs in OpenCL have been developed and offered by FPGA vendors that reduce the programming effort required. These improvements reveal the possibility of implementing a concept to enable on-the-fly offloading computation at which CPUs/GPUs perform poorly to FPGAs while performing low-latency data movement. We think that this concept is key to improving the performance of heterogeneous supercomputers using accelerators such as the GPU. In this paper, we propose a GPU-FPGA-accelerated simulation based on the concept and show our implementation with CUDA and OpenCL mixed programming for the proposed method. The results of experiments show that our proposed method can always achieve a better performance than GPU-based implementation and we believe that realizing GPU-FPGA-accelerated simulation is the most significant difference between our work and previous studies.